class: inverse, middle, left, my-title-slide, title-slide .title[ # Ecological forecasting in R ] .subtitle[ ## Lecture 4: evaluating dynamic models ] .author[ ### Nicholas Clark ] .institute[ ### School of Veterinary Science, University of Queensland ] .date[ ### 0900–1200 CET Wednesday 26th March, 2025 ] --- <style>:root{--panel-tab-foreground:#8F2727;--panel-tab-inactive-opacity:0.8;}</style> ## Workflow Press the "o" key on your keyboard to navigate among slides Access the [tutorial html here](https://nicholasjclark.github.io/physalia-forecasting-course/day3/tutorial_3_physalia) - Download the data objects and exercise <svg aria-hidden="true" role="img" viewBox="0 0 581 512" style="height:1em;width:1.13em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:steelblue;overflow:visible;position:relative;"><path d="M581 226.6C581 119.1 450.9 32 290.5 32S0 119.1 0 226.6C0 322.4 103.3 402 239.4 418.1V480h99.1v-61.5c24.3-2.7 47.6-7.4 69.4-13.9L448 480h112l-67.4-113.7c54.5-35.4 88.4-84.9 88.4-139.7zm-466.8 14.5c0-73.5 98.9-133 220.8-133s211.9 40.7 211.9 133c0 50.1-26.5 85-70.3 106.4-2.4-1.6-4.7-2.9-6.4-3.7-10.2-5.2-27.8-10.5-27.8-10.5s86.6-6.4 86.6-92.7-90.6-87.9-90.6-87.9h-199V361c-74.1-21.5-125.2-67.1-125.2-119.9zm225.1 38.3v-55.6c57.8 0 87.8-6.8 87.8 27.3 0 36.5-38.2 28.3-87.8 28.3zm-.9 72.5H365c10.8 0 18.9 11.7 24 19.2-16.1 1.9-33 2.8-50.6 2.9v-22.1z"/></svg> script from the html file - Complete exercises and use Slack to ask questions Relevant open-source materials include: - [Evaluating distributional forecasts](https://www.youtube.com/watch?v=prZH2TyrRYs&t=1s) - [Approximate leave-future-out cross-validation for Bayesian time series models](https://cran.r-project.org/web/packages/loo/vignettes/loo2-lfo.html) - [The Marginal Effects Zoo (0.14.0)](https://marginaleffects.com/) --- ## This lecture's topics Forecasting from dynamic models Prediction-based inferences Bayesian posterior predictive checks Probabilistic forecast evaluation --- class: inverse middle center big-subsection # Forecasting from dynamic models --- ## Forecasting in `mvgam` Two options - Pass `newdata` into the `mvgam()` function for automatic probabilistic forecasts through `Stan` - Produce forecasts outside of `Stan` by passing `newdata` and the fitted model to the `forecast()` function Both require any out-of-sample covariates to be supplied Both should give equivalent results --- ## Simulated data <img src="lecture_4_slidedeck_files/figure-html/unnamed-chunk-1-1.png" style="display: block; margin: auto;" /> --- ## The model ``` r library(mvgam) model <- mvgam( y ~ * s(season, bs = 'cc', k = 8), data = data_train, newdata = data_test, trend_model = GP(), family = poisson() ) ``` A cyclic smooth of `season` to capture repeated periodic variation --- ## The model ``` r library(mvgam) model <- mvgam( y ~ s(season, bs = 'cc', k = 8), data = data_train, newdata = data_test, * trend_model = GP(), family = poisson() ) ``` A Gaussian Process trend (approximated with [Hilbert basis functions](https://link.springer.com/article/10.1007/s11222-022-10167-2)) --- ## The model ``` r library(mvgam) model <- mvgam( y ~ s(season, bs = 'cc', k = 8), data = data_train, * newdata = data_test, trend_model = GP(), family = poisson() ) ``` Forecasts computed automatically using the [`generated quantities` block in `Stan`](https://mc-stan.org/docs/reference-manual/program-block-generated-quantities.html) --- ## Dropping `newdata` ``` r model2 <- mvgam( y ~ s(season, bs = 'cc', k = 8), data = data_train, trend_model = GP(), family = poisson() ) ``` Predictions will only be calculated for the training data if no testing data (i.e. `newdata`) are supplied --- `plot(model, type = 'trend', newdata = data_test)` <img src="lecture_4_slidedeck_files/figure-html/unnamed-chunk-6-1.png" style="display: block; margin: auto;" /> Trend extends into the future --- `plot(forecast(model))` <img src="lecture_4_slidedeck_files/figure-html/unnamed-chunk-7-1.png" style="display: block; margin: auto;" /> Forecasts can be compared to truths quickly --- `plot(hindcast(model2))` <img src="lecture_4_slidedeck_files/figure-html/unnamed-chunk-8-1.png" style="display: block; margin: auto;" /> No forecasts available. Now what? --- ## Posterior draws Dynamic `mvgam` models contain draws for many quantities - `\(\beta\)` coefficients for linear predictor terms (called `b`) - Any family-specific shape / scale parameters (i.e. `\(\phi\)` for Negative Binomial; `\(\sigma_{obs}\)` for Normal / LogNormal etc...) - Any trend-specific parameters (i.e. `\(\alpha\)` and `\(\rho\)` for GP trends; `\(\sigma\)` and `\(ar1\)` for AR trends etc...) - In-sample posterior predictions (called `ypred`) - In-sample posterior trend estimates (called `trend`) All stored as MCMC draws in an object of class `stanfit` in the `model_output` slot --- # The `stanfit` object ``` r summary(model2$model_output) ``` ``` ## $summary ## mean se_mean sd 2.5% 25% ## alpha_gp[1] 0.62171563 0.006264558 0.1927977 3.259427e-01 0.4759840000 ## rho_gp[1] 12.69452436 0.472567665 9.0984607 2.409932e+00 6.6534600000 ## b_gp[1,1] -0.08784042 0.028832518 0.9571218 -1.970965e+00 -0.7333785000 ## b_gp[2,1] 1.03580834 0.018317140 0.7738592 -4.485449e-01 0.5047912500 ## b_gp[3,1] 0.55880067 0.021205927 0.8509277 -1.161346e+00 -0.0172447250 ## b_gp[4,1] -1.22545951 0.021101693 0.8203285 -2.905063e+00 -1.7379950000 ## b_gp[5,1] -0.68120807 0.019720616 0.7682425 -2.147765e+00 -1.2233075000 ## b_gp[6,1] 0.58285264 0.021051423 0.8264262 -9.898045e-01 0.0222727500 ## b_gp[7,1] 0.23068307 0.019710134 0.8508540 -1.432141e+00 -0.3553967500 ## b_gp[8,1] 0.11852579 0.021177339 0.8353253 -1.565237e+00 -0.4458395000 ## b_gp[9,1] 0.33095648 0.019470049 0.8352777 -1.283770e+00 -0.2210705000 ## b_gp[10,1] -0.17751874 0.020550968 0.8664645 -1.799261e+00 -0.7721652500 ## b_gp[11,1] -0.58467981 0.022633968 0.9228061 -2.328848e+00 -1.2267625000 ## b_gp[12,1] -0.02275813 0.019498238 0.8754558 -1.769344e+00 -0.5927065000 ## b_gp[13,1] 0.49333417 0.025280945 0.9395104 -1.480099e+00 -0.1008087500 ## b_gp[14,1] 0.21716815 0.020045951 0.9122011 -1.573494e+00 -0.3939732500 ## b_gp[15,1] -0.36779992 0.022067195 0.9359502 -2.210335e+00 -0.9861385000 ## b_gp[16,1] -0.13425582 0.020625736 0.9270740 -1.951685e+00 -0.7626875000 ## b_gp[17,1] 0.31248331 0.020502972 0.9629600 -1.459442e+00 -0.3614110000 ## b_gp[18,1] 0.06279521 0.019464016 0.9254722 -1.747920e+00 -0.5422437500 ## b_gp[19,1] -0.22473476 0.022094831 0.9508665 -2.066299e+00 -0.8647735000 ## b_gp[20,1] -0.04984579 0.018908843 0.9844381 -1.944102e+00 -0.7020175000 ## lambda[1] 40.39139599 0.393266601 18.0150055 1.099391e+01 27.2295500000 ## trend[1,1] 0.64273882 0.012657805 0.3996688 -1.179294e-01 0.3871987500 ## trend[2,1] 0.67319650 0.012674730 0.3913616 -6.203647e-02 0.4342960000 ## trend[3,1] 0.70006801 0.012790899 0.3863337 -3.934935e-02 0.4664472500 ## trend[4,1] 0.72304255 0.012987833 0.3841991 -2.358478e-02 0.4908587500 ## trend[5,1] 0.74176079 0.013245847 0.3843098 -2.850593e-02 0.5159542500 ## trend[6,1] 0.75578675 0.013544247 0.3859214 -2.985536e-02 0.5399045000 ## trend[7,1] 0.76459753 0.013861683 0.3883638 -4.485834e-02 0.5504362500 ## trend[8,1] 0.76759415 0.014176447 0.3911453 -5.780767e-02 0.5547317500 ## trend[9,1] 0.76413367 0.014466609 0.3939609 -7.397913e-02 0.5523895000 ## trend[10,1] 0.75358232 0.014710372 0.3966239 -9.675346e-02 0.5405170000 ## trend[11,1] 0.73538506 0.014907677 0.3989652 -1.254118e-01 0.5296720000 ## trend[12,1] 0.70914507 0.015024948 0.4007615 -1.643104e-01 0.4911690000 ## trend[13,1] 0.67470519 0.015029266 0.4017354 -1.869224e-01 0.4506540000 ## trend[14,1] 0.63222067 0.014917994 0.4016327 -2.208771e-01 0.4063277500 ## trend[15,1] 0.58221661 0.014708082 0.4003499 -2.605171e-01 0.3550415000 ## trend[16,1] 0.52561819 0.014405779 0.3980508 -2.964800e-01 0.3029405000 ## trend[17,1] 0.46375046 0.014111355 0.3952162 -3.267151e-01 0.2440652500 ## trend[18,1] 0.39830181 0.013840715 0.3925750 -3.670081e-01 0.1791775000 ## trend[19,1] 0.33125186 0.013636491 0.3909137 -4.239480e-01 0.1063397500 ## trend[20,1] 0.26476620 0.013529714 0.3908089 -4.753986e-01 0.0351599250 ## trend[21,1] 0.20106514 0.013525620 0.3923874 -5.247949e-01 -0.0327384250 ## trend[22,1] 0.14227535 0.013600936 0.3952328 -5.693974e-01 -0.0910937500 ## trend[23,1] 0.09027647 0.013712018 0.3984959 -6.356912e-01 -0.1497592500 ## trend[24,1] 0.04655556 0.013810530 0.4011732 -6.915866e-01 -0.1945110000 ## trend[25,1] 0.01208216 0.013860874 0.4024477 -7.313551e-01 -0.2259050000 ## trend[26,1] -0.01278390 0.013853867 0.4019768 -7.527962e-01 -0.2492127500 ## trend[27,1] -0.02834274 0.013813557 0.4000540 -7.722916e-01 -0.2583062500 ## trend[28,1] -0.03555658 0.013794568 0.3975926 -8.055365e-01 -0.2653267500 ## trend[29,1] -0.03600075 0.013868205 0.3959163 -8.153499e-01 -0.2678885000 ## trend[30,1] -0.03176677 0.014097950 0.3963717 -8.504498e-01 -0.2591177500 ## trend[31,1] -0.02532236 0.014512363 0.3998649 -8.610054e-01 -0.2542077500 ## trend[32,1] -0.01933923 0.015127908 0.4064973 -8.973470e-01 -0.2519047500 ## trend[33,1] -0.01650112 0.015881463 0.4154748 -9.452750e-01 -0.2479775000 ## trend[34,1] -0.01930712 0.016680251 0.4253241 -9.595847e-01 -0.2570537500 ## trend[35,1] -0.02988562 0.017334367 0.4342996 -9.889636e-01 -0.2761030000 ## trend[36,1] -0.04983381 0.017722835 0.4408062 -1.025648e+00 -0.2994722500 ## trend[37,1] -0.08009532 0.017796777 0.4437233 -1.064071e+00 -0.3276435000 ## trend[38,1] -0.12088615 0.017563943 0.4425970 -1.091899e+00 -0.3646085000 ## trend[39,1] -0.17167442 0.017056683 0.4377060 -1.127096e+00 -0.4125015000 ## trend[40,1] -0.23121550 0.016337403 0.4300138 -1.154369e+00 -0.4622632500 ## trend[41,1] -0.29763941 0.015508068 0.4210105 -1.180046e+00 -0.5267387500 ## trend[42,1] -0.36858309 0.014747549 0.4124370 -1.205619e+00 -0.5914420000 ## trend[43,1] -0.44135687 0.014140251 0.4059113 -1.265820e+00 -0.6607722500 ## trend[44,1] -0.51313154 0.013724734 0.4025268 -1.331401e+00 -0.7390512500 ## trend[45,1] -0.58113055 0.013527252 0.4025621 -1.385912e+00 -0.8149390000 ## trend[46,1] -0.64281328 0.013515076 0.4054366 -1.447202e+00 -0.8772287500 ## trend[47,1] -0.69603430 0.013613723 0.4099416 -1.518664e+00 -0.9336040000 ## trend[48,1] -0.73916816 0.013737433 0.4146341 -1.570491e+00 -0.9864800000 ## trend[49,1] -0.77118978 0.013816782 0.4182343 -1.601439e+00 -1.0326800000 ## trend[50,1] -0.79170729 0.013814652 0.4199111 -1.615091e+00 -1.0482400000 ## trend[51,1] -0.80094581 0.013730420 0.4194190 -1.631642e+00 -1.0513800000 ## trend[52,1] -0.79968680 0.013595090 0.4170901 -1.604515e+00 -1.0453700000 ## trend[53,1] -0.78916862 0.013459611 0.4137020 -1.600936e+00 -1.0390350000 ## trend[54,1] -0.77095996 0.013378519 0.4102514 -1.591946e+00 -1.0166225000 ## trend[55,1] -0.74681707 0.013392445 0.4076796 -1.576380e+00 -0.9915065000 ## trend[56,1] -0.71853743 0.013515217 0.4066227 -1.547603e+00 -0.9521127500 ## trend[57,1] -0.68782252 0.013730917 0.4072662 -1.530976e+00 -0.9180970000 ## trend[58,1] -0.65616080 0.014001686 0.4093555 -1.507104e+00 -0.8851047500 ## trend[59,1] -0.62473826 0.014281346 0.4123397 -1.487745e+00 -0.8655475000 ## trend[60,1] -0.59438398 0.014549337 0.4155797 -1.485086e+00 -0.8350400000 ## trend[61,1] -0.56555118 0.014748442 0.4185265 -1.458803e+00 -0.7987910000 ## trend[62,1] -0.53833449 0.014867938 0.4208202 -1.430404e+00 -0.7796560000 ## trend[63,1] -0.51251770 0.014913079 0.4222950 -1.417599e+00 -0.7583077500 ## trend[64,1] -0.48764671 0.014899720 0.4229240 -1.399610e+00 -0.7353657500 ## trend[65,1] -0.46311855 0.014848292 0.4227485 -1.381107e+00 -0.7078310000 ## trend[66,1] -0.43827719 0.014778566 0.4218349 -1.358319e+00 -0.6772102500 ## trend[67,1] -0.41250654 0.014716047 0.4202843 -1.324771e+00 -0.6496577500 ## trend[68,1] -0.38531267 0.014671099 0.4182872 -1.267957e+00 -0.6158282500 ## trend[69,1] -0.35638743 0.014646801 0.4161903 -1.245275e+00 -0.5885595000 ## trend[70,1] -0.32564890 0.014649258 0.4145281 -1.221397e+00 -0.5533397500 ## trend[71,1] -0.29325639 0.014682906 0.4139810 -1.189639e+00 -0.5227470000 ## trend[72,1] -0.25959986 0.014750079 0.4152499 -1.142997e+00 -0.4993935000 ## trend[73,1] -0.22526644 0.014849749 0.4188820 -1.082581e+00 -0.4713192500 ## trend[74,1] -0.19098805 0.014976267 0.4251155 -1.061539e+00 -0.4452245000 ## trend[75,1] -0.15757711 0.015119202 0.4338213 -1.050154e+00 -0.4312905000 ## diag_SPD[1,1] 3.28317300 0.078239287 1.7100723 1.324870e+00 2.0737225000 ## diag_SPD[2,1] 3.03330312 0.055152663 1.3237375 1.313451e+00 2.0452125000 ## diag_SPD[3,1] 2.71517422 0.034096283 1.0063526 1.289930e+00 1.9712900000 ## diag_SPD[4,1] 2.39621018 0.026671399 0.8558161 1.105898e+00 1.7935875000 ## diag_SPD[5,1] 2.10755793 0.029961096 0.8105344 5.718486e-01 1.5748825000 ## diag_SPD[6,1] 1.85611392 0.034224827 0.7968573 1.892141e-01 1.3865950000 ## diag_SPD[7,1] 1.63887409 0.036532237 0.7844825 5.019058e-02 1.2081250000 ## diag_SPD[8,1] 1.45059748 0.037142644 0.7672847 1.127289e-02 1.0060850000 ## diag_SPD[9,1] 1.28652840 0.036934895 0.7459976 2.195503e-03 0.8110107500 ## diag_SPD[10,1] 1.14291239 0.036134362 0.7223050 3.377533e-04 0.6031347500 ## diag_SPD[11,1] 1.01684020 0.034888416 0.6975283 4.030934e-05 0.4202860000 ## diag_SPD[12,1] 0.90600159 0.033394778 0.6725144 3.921070e-06 0.2797527500 ## diag_SPD[13,1] 0.80849554 0.031784842 0.6477513 3.111350e-07 0.1774105000 ## diag_SPD[14,1] 0.72270795 0.030144595 0.6234991 2.015840e-08 0.1112277500 ## diag_SPD[15,1] 0.64723484 0.028528672 0.5998881 1.066420e-09 0.0678447250 ## diag_SPD[16,1] 0.58083620 0.026969988 0.5769800 4.606400e-11 0.0396164250 ## diag_SPD[17,1] 0.52240941 0.025486574 0.5548022 1.624650e-12 0.0220959750 ## diag_SPD[18,1] 0.47097160 0.024086497 0.5333641 4.678660e-14 0.0115367000 ## diag_SPD[19,1] 0.42564872 0.022771457 0.5126656 1.100140e-15 0.0058832150 ## diag_SPD[20,1] 0.38566603 0.021539333 0.4927012 2.112200e-17 0.0029063650 ## SPD_beta[1,1] -0.25043069 0.134495149 3.5950137 -7.567005e+00 -2.0420975000 ## SPD_beta[2,1] 2.82850218 0.065079283 2.1819166 -1.361019e+00 1.4384975000 ## SPD_beta[3,1] 1.49655394 0.075682479 2.4813073 -3.213900e+00 -0.0327996000 ## SPD_beta[4,1] -2.69664493 0.051449542 1.9227890 -6.613854e+00 -3.8343825000 ## SPD_beta[5,1] -1.36484122 0.045640109 1.6745556 -4.766739e+00 -2.4387425000 ## SPD_beta[6,1] 1.10343435 0.046881433 1.6921909 -1.912549e+00 0.0184664750 ## SPD_beta[7,1] 0.41294027 0.036725850 1.4458354 -2.276592e+00 -0.4471775000 ## SPD_beta[8,1] 0.15947856 0.031497476 1.2401495 -2.411912e+00 -0.4921335000 ## SPD_beta[9,1] 0.49843205 0.027577220 1.1532614 -1.675175e+00 -0.1042947500 ## SPD_beta[10,1] -0.26789095 0.026683208 1.1041756 -2.647325e+00 -0.8195695000 ## SPD_beta[11,1] -0.67309808 0.030700645 1.0958447 -3.047747e+00 -1.2731325000 ## SPD_beta[12,1] -0.03141144 0.019983183 0.8781761 -1.963642e+00 -0.4052025000 ## SPD_beta[13,1] 0.47380571 0.023477093 0.8640423 -9.537333e-01 -0.0001220795 ## SPD_beta[14,1] 0.23582879 0.019242177 0.8309073 -1.225463e+00 -0.0745084000 ## SPD_beta[15,1] -0.28686711 0.018308427 0.7429964 -2.118299e+00 -0.5846245000 ## SPD_beta[16,1] -0.11055553 0.012967688 0.6479840 -1.615814e+00 -0.3232557500 ## SPD_beta[17,1] 0.25182972 0.018791050 0.7273158 -8.487650e-01 -0.0098425050 ## SPD_beta[18,1] 0.03482001 0.012857229 0.5636826 -1.238808e+00 -0.0678196750 ## SPD_beta[19,1] -0.17808778 0.014549915 0.5592318 -1.700905e+00 -0.2813735000 ## SPD_beta[20,1] -0.04173846 0.011448973 0.4903129 -1.319493e+00 -0.1105472500 ## b[1] 1.01523000 0.013639259 0.3734884 3.015096e-01 0.7966930000 ## b[2] -0.35924272 0.003378415 0.1458773 -6.633094e-01 -0.4553197500 ## b[3] -0.39592206 0.003615692 0.1694475 -7.306799e-01 -0.5045825000 ## b[4] -0.15715021 0.003499235 0.1627171 -4.793901e-01 -0.2701747500 ## b[5] 0.15367187 0.002947726 0.1438361 -1.403420e-01 0.0599692750 ## b[6] 0.56921740 0.002819677 0.1397529 3.054691e-01 0.4690540000 ## b[7] 0.39567916 0.002786008 0.1385199 1.277650e-01 0.3042747500 ## mus[1,1] 1.61365129 0.007334584 0.2700431 1.046350e+00 1.4395875000 ## mus[2,1] 1.41046929 0.006467622 0.2361283 9.259106e-01 1.2536450000 ## mus[3,1] 1.30290606 0.005784611 0.2202415 8.678680e-01 1.1611400000 ## mus[4,1] 1.32222334 0.005190356 0.2161126 8.939030e-01 1.1787875000 ## mus[5,1] 1.46625719 0.004341250 0.1974928 1.059196e+00 1.3407075000 ## mus[6,1] 1.65300983 0.003931188 0.1877807 1.259217e+00 1.5340525000 ## mus[7,1] 1.85174209 0.003573326 0.1714417 1.520212e+00 1.7327975000 ## mus[8,1] 2.14642180 0.003324872 0.1580859 1.825606e+00 2.0447700000 ## mus[9,1] 2.35114969 0.003716881 0.1631647 2.018326e+00 2.2431125000 ## mus[10,1] 2.25281256 0.003942581 0.1634679 1.929488e+00 2.1484250000 ## mus[11,1] 1.98553534 0.004069358 0.1631868 1.663543e+00 1.8749150000 ## mus[12,1] 1.68005771 0.004140611 0.1718828 1.341878e+00 1.5670450000 ## mus[13,1] 1.64561771 0.004123518 0.1730929 1.314802e+00 1.5334350000 ## mus[14,1] 1.36949342 0.004651005 0.1904571 9.841213e-01 1.2401475000 ## mus[15,1] 1.18505478 0.005136846 0.2107762 7.668765e-01 1.0460975000 ## mus[16,1] 1.12479888 0.005011099 0.2227969 6.982289e-01 0.9832127500 ## mus[17,1] 1.18824679 0.004824755 0.2136750 7.676711e-01 1.0424500000 ## mus[18,1] 1.29552495 0.004918482 0.2122536 8.630107e-01 1.1574750000 ## mus[19,1] 1.41839661 0.004796935 0.2022571 9.993715e-01 1.2904000000 ## mus[20,1] 1.64359390 0.005191376 0.1942657 1.240411e+00 1.5168250000 ## mus[21,1] 1.78808103 0.006359843 0.2057567 1.373367e+00 1.6558950000 ## mus[22,1] 1.64150564 0.007119387 0.2157274 1.202824e+00 1.5001650000 ## mus[23,1] 1.34042678 0.007536798 0.2237585 8.743199e-01 1.1929625000 ## mus[24,1] 1.01746806 0.007779693 0.2367349 5.257291e-01 0.8704147500 ## mus[25,1] 0.98299469 0.007769531 0.2401418 4.757799e-01 0.8338182500 ## mus[26,1] 0.72448879 0.007618039 0.2495410 1.719943e-01 0.5751935000 ## mus[27,1] 0.57449539 0.007159381 0.2548998 1.778944e-02 0.4118712500 ## mus[28,1] 0.56362420 0.006236736 0.2518571 3.433839e-02 0.4040602500 ## mus[29,1] 0.68849569 0.005413530 0.2296699 2.051638e-01 0.5508515000 ## mus[30,1] 0.86545628 0.004779796 0.2176936 4.181816e-01 0.7292195000 ## mus[31,1] 1.06182242 0.004562780 0.2048866 6.492649e-01 0.9268267500 ## mus[32,1] 1.35948835 0.004959684 0.1939527 9.758914e-01 1.2313925000 ## mus[33,1] 1.57051469 0.005625946 0.2038617 1.172781e+00 1.4306125000 ## mus[34,1] 1.47992324 0.006332757 0.2178982 1.061557e+00 1.3303650000 ## mus[35,1] 1.22026466 0.007219167 0.2263897 7.869639e-01 1.0632675000 ## mus[36,1] 0.92107875 0.007754379 0.2364171 4.803779e-01 0.7593072500 ## mus[37,1] 0.89081719 0.007929418 0.2415082 4.381307e-01 0.7252730000 ## mus[38,1] 0.61638652 0.008124192 0.2515862 1.294063e-01 0.4424452500 ## mus[39,1] 0.43116371 0.007944556 0.2610635 -6.466624e-02 0.2546182500 ## mus[40,1] 0.36796521 0.007184958 0.2633682 -1.406598e-01 0.1888640000 ## mus[41,1] 0.42685699 0.006077544 0.2440919 -6.136666e-02 0.2625512500 ## mus[42,1] 0.52863998 0.005299715 0.2336607 5.989643e-02 0.3719577500 ## mus[43,1] 0.64578777 0.004663180 0.2265603 1.966833e-01 0.4927730000 ## mus[44,1] 0.86569607 0.004716744 0.2259923 3.845766e-01 0.7226702500 ## mus[45,1] 1.00588544 0.006151045 0.2408193 4.964396e-01 0.8528867500 ## mus[46,1] 0.85641709 0.007303965 0.2523248 3.149678e-01 0.6959197500 ## mus[47,1] 0.55411601 0.008243884 0.2641979 -1.513974e-02 0.3964065000 ## mus[48,1] 0.23174434 0.008667330 0.2788468 -3.599612e-01 0.0595755750 ## mus[49,1] 0.19972269 0.009063259 0.2870133 -4.108049e-01 0.0180223500 ## mus[50,1] -0.05443465 0.009030240 0.2950099 -6.987269e-01 -0.2402992500 ## mus[51,1] -0.19810769 0.008718279 0.3061593 -8.573136e-01 -0.3871335000 ## mus[52,1] -0.20050607 0.008277795 0.3136368 -8.695932e-01 -0.4008192500 ## mus[53,1] -0.06467220 0.007590370 0.2963559 -6.914219e-01 -0.2590750000 ## mus[54,1] 0.12626310 0.006798478 0.2800108 -4.587700e-01 -0.0615637000 ## mus[55,1] 0.34032761 0.005804743 0.2599245 -2.030381e-01 0.1725640000 ## mus[56,1] 0.66029024 0.005290563 0.2440977 1.472036e-01 0.5029385000 ## mus[57,1] 0.89919344 0.005146818 0.2444417 4.053608e-01 0.7421497500 ## mus[58,1] 0.84306940 0.005020667 0.2420866 3.502416e-01 0.6873400000 ## mus[59,1] 0.62541204 0.004943758 0.2361028 1.548745e-01 0.4693770000 ## mus[60,1] 0.37652855 0.005048541 0.2365042 -9.048120e-02 0.2242130000 ## mus[61,1] 0.40536129 0.005121430 0.2366893 -6.540626e-02 0.2512875000 ## mus[62,1] 0.19893813 0.005869826 0.2472424 -2.796962e-01 0.0404066250 ## mus[63,1] 0.09032043 0.006385983 0.2611403 -4.030187e-01 -0.0864134000 ## mus[64,1] 0.11153403 0.006370561 0.2687434 -4.422454e-01 -0.0630572250 ## mus[65,1] 0.26137784 0.006099582 0.2571885 -2.689249e-01 0.0871347250 ## mus[66,1] 0.45894587 0.005393403 0.2512018 -5.894086e-02 0.2952910000 ## mus[67,1] 0.67463813 0.004974299 0.2393751 1.628184e-01 0.5150555000 ## mus[68,1] 0.99351494 0.004800733 0.2248437 5.335621e-01 0.8467055000 ## mus[69,1] 1.23062854 0.004717602 0.2236062 7.951170e-01 1.0786200000 ## mus[70,1] 1.17358136 0.004789417 0.2251858 7.221206e-01 1.0237125000 ## mus[71,1] 0.95689389 0.005071203 0.2260130 5.028874e-01 0.8121870000 ## mus[72,1] 0.71131265 0.005268848 0.2345799 2.394187e-01 0.5603140000 ## mus[73,1] 0.74564610 0.005518041 0.2506747 2.345564e-01 0.5837080000 ## mus[74,1] 0.54628462 0.005967401 0.2781405 -1.324516e-02 0.3648892500 ## mus[75,1] 0.44526099 0.006857098 0.3172072 -1.793546e-01 0.2330677500 ## rho[1] 3.58761515 0.013103628 0.4976427 2.397342e+00 3.3043025000 ## ypred[1,1] 5.20400000 0.074035800 2.6179784 1.000000e+00 3.0000000000 ## ypred[2,1] 4.19150000 0.048087984 2.2731941 9.750000e-01 3.0000000000 ## ypred[3,1] 3.79650000 0.047984026 2.1124202 0.000000e+00 2.0000000000 ## ypred[4,1] 3.86850000 0.049592264 2.0972379 0.000000e+00 2.0000000000 ## ypred[5,1] 4.41850000 0.050677119 2.2534189 1.000000e+00 3.0000000000 ## ypred[6,1] 5.24650000 0.057885803 2.5258519 1.000000e+00 3.0000000000 ## ypred[7,1] 6.45200000 0.062799681 2.7875762 2.000000e+00 4.0000000000 ## ypred[8,1] 8.65150000 0.074016301 3.2813765 3.000000e+00 6.0000000000 ## ypred[9,1] 10.66300000 0.082112166 3.7012539 4.000000e+00 8.0000000000 ## ypred[10,1] 9.60850000 0.080432354 3.5810110 4.000000e+00 7.0000000000 ## ypred[11,1] 7.36650000 0.063558955 2.9215485 2.000000e+00 5.0000000000 ## ypred[12,1] 5.40200000 0.062288709 2.5350758 1.000000e+00 4.0000000000 ## ypred[13,1] 5.27650000 0.057542784 2.4615193 1.000000e+00 4.0000000000 ## ypred[14,1] 4.07100000 0.053021488 2.1834245 0.000000e+00 3.0000000000 ## ypred[15,1] 3.33000000 0.043886756 1.9824392 0.000000e+00 2.0000000000 ## ypred[16,1] 3.11850000 0.042445987 1.8534226 0.000000e+00 2.0000000000 ## ypred[17,1] 3.39800000 0.042069760 1.9181855 0.000000e+00 2.0000000000 ## ypred[18,1] 3.73250000 0.046031100 2.0971750 0.000000e+00 2.0000000000 ## ypred[19,1] 4.28450000 0.051381443 2.2527977 1.000000e+00 3.0000000000 ## ypred[20,1] 5.22650000 0.056054812 2.4882310 1.000000e+00 3.0000000000 ## ypred[21,1] 6.14850000 0.061009170 2.7631984 1.975000e+00 4.0000000000 ## ypred[22,1] 5.27450000 0.064123713 2.5949020 1.000000e+00 3.0000000000 ## ypred[23,1] 3.84500000 0.052107199 2.1452916 0.000000e+00 2.0000000000 ## ypred[24,1] 2.84150000 0.044040720 1.8069339 0.000000e+00 2.0000000000 ## ypred[25,1] 2.72150000 0.041298921 1.7650766 0.000000e+00 1.0000000000 ## ypred[26,1] 2.14150000 0.035746834 1.4941868 0.000000e+00 1.0000000000 ## ypred[27,1] 1.81400000 0.033672894 1.4482585 0.000000e+00 1.0000000000 ## ypred[28,1] 1.76450000 0.031627775 1.4226917 0.000000e+00 1.0000000000 ## ypred[29,1] 2.02100000 0.033582736 1.5002281 0.000000e+00 1.0000000000 ## ypred[30,1] 2.46900000 0.038784294 1.7267107 0.000000e+00 1.0000000000 ## ypred[31,1] 2.96200000 0.043043325 1.8265334 0.000000e+00 2.0000000000 ## ypred[32,1] 3.95250000 0.048700006 2.1015356 0.000000e+00 2.0000000000 ## ypred[33,1] 4.87300000 0.055634423 2.4328647 1.000000e+00 3.0000000000 ## ypred[34,1] 4.62150000 0.060908276 2.4114612 1.000000e+00 3.0000000000 ## ypred[35,1] 3.53700000 0.050153460 2.0473707 0.000000e+00 2.0000000000 ## ypred[36,1] 2.53550000 0.041855595 1.7149957 0.000000e+00 1.0000000000 ## ypred[37,1] 2.54000000 0.040179121 1.7146049 0.000000e+00 1.0000000000 ## ypred[38,1] 1.88100000 0.036601968 1.4480633 0.000000e+00 1.0000000000 ## ypred[39,1] 1.60400000 0.030902908 1.3660590 0.000000e+00 1.0000000000 ## ypred[40,1] 1.48000000 0.031789688 1.2831302 0.000000e+00 1.0000000000 ## ypred[41,1] 1.62900000 0.028952614 1.3480607 0.000000e+00 1.0000000000 ## ypred[42,1] 1.72050000 0.032042822 1.3911676 0.000000e+00 1.0000000000 ## ypred[43,1] 1.95900000 0.032854388 1.4874223 0.000000e+00 1.0000000000 ## ypred[44,1] 2.46550000 0.040233700 1.6733828 0.000000e+00 1.0000000000 ## ypred[45,1] 2.80150000 0.041642382 1.8173467 0.000000e+00 1.0000000000 ## ypred[46,1] 2.44800000 0.042509427 1.6830664 0.000000e+00 1.0000000000 ## ypred[47,1] 1.81550000 0.032932944 1.4357892 0.000000e+00 1.0000000000 ## ypred[48,1] 1.33050000 0.028789825 1.2397735 0.000000e+00 0.0000000000 ## ypred[49,1] 1.29650000 0.027406560 1.1892413 0.000000e+00 0.0000000000 ## ypred[50,1] 0.96100000 0.023586890 1.0143932 0.000000e+00 0.0000000000 ## ypred[51,1] 0.81100000 0.022808225 0.9272049 0.000000e+00 0.0000000000 ## ypred[52,1] 0.84750000 0.020722151 0.9395132 0.000000e+00 0.0000000000 ## ypred[53,1] 0.95650000 0.023592581 0.9975496 0.000000e+00 0.0000000000 ## ypred[54,1] 1.19950000 0.027107906 1.1577435 0.000000e+00 0.0000000000 ## ypred[55,1] 1.46200000 0.029736871 1.2519344 0.000000e+00 1.0000000000 ## ypred[56,1] 1.96550000 0.031015309 1.4513314 0.000000e+00 1.0000000000 ## ypred[57,1] 2.51100000 0.037028661 1.7091927 0.000000e+00 1.0000000000 ## ypred[58,1] 2.35000000 0.036398380 1.6385489 0.000000e+00 1.0000000000 ## ypred[59,1] 1.93200000 0.031760794 1.4766402 0.000000e+00 1.0000000000 ## ypred[60,1] 1.50600000 0.028313761 1.2856090 0.000000e+00 1.0000000000 ## ypred[61,1] 1.56900000 0.028801536 1.3008017 0.000000e+00 1.0000000000 ## ypred[62,1] 1.21500000 0.025217727 1.1456139 0.000000e+00 0.0000000000 ## ypred[63,1] 1.12600000 0.025708282 1.1102884 0.000000e+00 0.0000000000 ## ypred[64,1] 1.15350000 0.026061919 1.1513473 0.000000e+00 0.0000000000 ## ypred[65,1] 1.35600000 0.029369673 1.2120225 0.000000e+00 0.0000000000 ## ypred[66,1] 1.59550000 0.032502249 1.3666798 0.000000e+00 1.0000000000 ## ypred[67,1] 2.02400000 0.036261366 1.4931640 0.000000e+00 1.0000000000 ## ypred[68,1] 2.73150000 0.039754546 1.8105377 0.000000e+00 1.0000000000 ## ypred[69,1] 3.48300000 0.044611398 2.0682964 0.000000e+00 2.0000000000 ## ypred[70,1] 3.33200000 0.043820894 1.9595142 0.000000e+00 2.0000000000 ## ypred[71,1] 2.67000000 0.037521852 1.7299122 0.000000e+00 1.0000000000 ## ypred[72,1] 2.11600000 0.033702007 1.5348361 0.000000e+00 1.0000000000 ## ypred[73,1] 2.23850000 0.035805139 1.6018429 0.000000e+00 1.0000000000 ## ypred[74,1] 1.82500000 0.033042263 1.4479030 0.000000e+00 1.0000000000 ## ypred[75,1] 1.62400000 0.030681283 1.3880156 0.000000e+00 1.0000000000 ## lp__ 67.40435230 0.210113079 4.6583609 5.770108e+01 64.3447500000 ## 50% 75% 97.5% n_eff Rhat ## alpha_gp[1] 5.916840e-01 7.380998e-01 1.04843825 947.1583 1.0009009 ## rho_gp[1] 9.872480e+00 1.587492e+01 37.43562750 370.6874 1.0017261 ## b_gp[1,1] -1.072840e-01 5.558110e-01 1.78952050 1101.9688 1.0031763 ## b_gp[2,1] 1.025785e+00 1.558720e+00 2.55206850 1784.8782 1.0022138 ## b_gp[3,1] 5.874040e-01 1.141060e+00 2.11864450 1610.1667 0.9996776 ## b_gp[4,1] -1.209170e+00 -6.886350e-01 0.38739460 1511.2662 0.9990524 ## b_gp[5,1] -6.779080e-01 -1.710062e-01 0.84519990 1517.5945 1.0013355 ## b_gp[6,1] 5.872130e-01 1.142280e+00 2.22596175 1541.1512 0.9995722 ## b_gp[7,1] 2.441520e-01 8.169033e-01 1.87483750 1863.5067 0.9991759 ## b_gp[8,1] 1.093055e-01 6.825177e-01 1.76302400 1555.8526 1.0001353 ## b_gp[9,1] 3.632390e-01 8.848037e-01 1.96046950 1840.4656 1.0011830 ## b_gp[10,1] -2.042815e-01 3.801408e-01 1.52014000 1777.6120 0.9989941 ## b_gp[11,1] -6.094450e-01 1.978300e-02 1.18584425 1662.2621 1.0016246 ## b_gp[12,1] -3.069480e-02 5.419323e-01 1.74363850 2015.9403 0.9991286 ## b_gp[13,1] 5.272285e-01 1.105722e+00 2.28021925 1381.0727 0.9999800 ## b_gp[14,1] 2.020040e-01 8.406807e-01 1.97383975 2070.7508 0.9995250 ## b_gp[15,1] -3.819375e-01 2.266710e-01 1.54344125 1798.9174 0.9994177 ## b_gp[16,1] -1.452280e-01 4.683083e-01 1.73949950 2020.2721 0.9993625 ## b_gp[17,1] 3.165570e-01 9.645455e-01 2.24191375 2205.8849 0.9997482 ## b_gp[18,1] 6.186390e-02 6.868677e-01 1.89368175 2260.7986 1.0004922 ## b_gp[19,1] -2.603430e-01 4.064470e-01 1.66637075 1852.0712 1.0002946 ## b_gp[20,1] -3.065770e-02 5.591552e-01 1.96300100 2710.4845 1.0005227 ## lambda[1] 3.861795e+01 5.166972e+01 80.58547250 2098.4309 1.0010791 ## trend[1,1] 6.388580e-01 8.565797e-01 1.49307750 996.9736 1.0037032 ## trend[2,1] 6.730120e-01 8.845370e-01 1.47776425 953.4081 1.0040936 ## trend[3,1] 6.977485e-01 9.142902e-01 1.50500875 912.2694 1.0043163 ## trend[4,1] 7.179400e-01 9.391070e-01 1.51093250 875.0631 1.0043701 ## trend[5,1] 7.425580e-01 9.601152e-01 1.50916675 841.7893 1.0042838 ## trend[6,1] 7.576845e-01 9.758243e-01 1.50605100 811.8728 1.0040997 ## trend[7,1] 7.687560e-01 9.859375e-01 1.48885225 784.9565 1.0038567 ## trend[8,1] 7.728685e-01 9.912745e-01 1.48581825 761.2746 1.0035819 ## trend[9,1] 7.755170e-01 9.943550e-01 1.47727200 741.6050 1.0032907 ## trend[10,1] 7.626400e-01 9.899175e-01 1.47858275 726.9599 1.0029913 ## trend[11,1] 7.472925e-01 9.699755e-01 1.46498125 716.2261 1.0026903 ## trend[12,1] 7.213570e-01 9.508830e-01 1.44685225 711.4527 1.0023960 ## trend[13,1] 6.857210e-01 9.127735e-01 1.42620025 714.5041 1.0021191 ## trend[14,1] 6.388195e-01 8.674580e-01 1.38329625 724.8318 1.0018714 ## trend[15,1] 5.897945e-01 8.167150e-01 1.33957925 740.9131 1.0016644 ## trend[16,1] 5.321790e-01 7.516820e-01 1.29275375 763.4905 1.0015085 ## trend[17,1] 4.685915e-01 6.861242e-01 1.24242675 784.3900 1.0014120 ## trend[18,1] 3.980630e-01 6.162150e-01 1.19299575 804.5041 1.0013805 ## trend[19,1] 3.275525e-01 5.519945e-01 1.13826225 821.7819 1.0014152 ## trend[20,1] 2.587900e-01 4.824725e-01 1.06731725 834.3564 1.0015104 ## trend[21,1] 1.948430e-01 4.210558e-01 1.01123650 841.6196 1.0016539 ## trend[22,1] 1.315480e-01 3.678207e-01 0.97018210 844.4391 1.0018290 ## trend[23,1] 8.037900e-02 3.144015e-01 0.91829357 844.5880 1.0020190 ## trend[24,1] 3.724260e-02 2.776195e-01 0.88745545 843.8072 1.0022100 ## trend[25,1] 5.500865e-03 2.461680e-01 0.84633232 843.0195 1.0023919 ## trend[26,1] -2.089460e-02 2.238617e-01 0.80935387 841.8987 1.0025570 ## trend[27,1] -3.789175e-02 2.132335e-01 0.77558385 838.7376 1.0026982 ## trend[28,1] -4.177790e-02 1.983837e-01 0.74602262 830.7311 1.0028081 ## trend[29,1] -3.976470e-02 1.942555e-01 0.71992460 815.0163 1.0028801 ## trend[30,1] -3.003020e-02 1.980700e-01 0.73347510 790.4847 1.0029118 ## trend[31,1] -1.809275e-02 2.056212e-01 0.74421210 759.1897 1.0029076 ## trend[32,1] -8.306025e-03 2.200753e-01 0.77925502 722.0339 1.0028792 ## trend[33,1] -2.672810e-03 2.316518e-01 0.80260947 684.3974 1.0028415 ## trend[34,1] -1.042713e-03 2.362023e-01 0.79636030 650.1819 1.0028075 ## trend[35,1] -7.910570e-03 2.293683e-01 0.79232395 627.7157 1.0027862 ## trend[36,1] -2.382750e-02 2.128412e-01 0.77109912 618.6272 1.0027830 ## trend[37,1] -5.638720e-02 1.899260e-01 0.73680015 621.6439 1.0028027 ## trend[38,1] -1.016770e-01 1.515867e-01 0.68807370 634.9989 1.0028518 ## trend[39,1] -1.565860e-01 9.950650e-02 0.63650315 658.5304 1.0029395 ## trend[40,1] -2.154360e-01 3.465752e-02 0.56030535 692.7855 1.0030768 ## trend[41,1] -2.778785e-01 -4.001025e-02 0.50546865 737.0051 1.0032729 ## trend[42,1] -3.469010e-01 -1.168170e-01 0.42654140 782.1239 1.0035281 ## trend[43,1] -4.193650e-01 -1.977437e-01 0.35541897 824.0396 1.0038270 ## trend[44,1] -4.963040e-01 -2.777035e-01 0.32228620 860.1651 1.0041361 ## trend[45,1] -5.722790e-01 -3.459540e-01 0.25699850 885.6184 1.0044134 ## trend[46,1] -6.401810e-01 -3.996460e-01 0.19643450 899.9305 1.0046232 ## trend[47,1] -6.984480e-01 -4.491400e-01 0.15126197 906.7554 1.0047483 ## trend[48,1] -7.433895e-01 -4.916250e-01 0.12433422 911.0011 1.0047905 ## trend[49,1] -7.756470e-01 -5.169458e-01 0.09443383 916.2744 1.0047622 ## trend[50,1] -7.880055e-01 -5.358340e-01 0.06083596 923.9211 1.0046784 ## trend[51,1] -7.971535e-01 -5.424262e-01 0.02740591 933.1007 1.0045509 ## trend[52,1] -7.992135e-01 -5.468335e-01 0.01376471 941.2297 1.0043871 ## trend[53,1] -7.847150e-01 -5.392318e-01 0.03311752 944.7355 1.0041906 ## trend[54,1] -7.654005e-01 -5.237780e-01 0.03242792 940.3383 1.0039652 ## trend[55,1] -7.378635e-01 -4.961155e-01 0.01970611 926.6555 1.0037183 ## trend[56,1] -7.093805e-01 -4.634078e-01 0.05742820 905.1845 1.0034634 ## trend[57,1] -6.783230e-01 -4.354915e-01 0.08464003 879.7467 1.0032194 ## trend[58,1] -6.401915e-01 -4.006053e-01 0.12550082 854.7529 1.0030059 ## trend[59,1] -6.097690e-01 -3.654410e-01 0.16879687 833.6276 1.0028385 ## trend[60,1] -5.782605e-01 -3.359402e-01 0.19947547 815.8722 1.0027255 ## trend[61,1] -5.502315e-01 -3.007755e-01 0.22516675 805.2926 1.0026663 ## trend[62,1] -5.204915e-01 -2.710282e-01 0.24595517 801.1092 1.0026522 ## trend[63,1] -5.025765e-01 -2.441830e-01 0.27311865 801.8576 1.0026683 ## trend[64,1] -4.824325e-01 -2.178200e-01 0.29792952 805.6910 1.0026957 ## trend[65,1] -4.581510e-01 -2.001593e-01 0.33194395 810.6083 1.0027138 ## trend[66,1] -4.308470e-01 -1.764430e-01 0.35309750 814.7426 1.0027040 ## trend[67,1] -4.031320e-01 -1.525810e-01 0.36723870 815.6501 1.0026509 ## trend[68,1] -3.757830e-01 -1.288420e-01 0.39452780 812.8753 1.0025445 ## trend[69,1] -3.367805e-01 -1.039455e-01 0.40247217 807.4180 1.0023802 ## trend[70,1] -3.030745e-01 -7.450647e-02 0.42770527 800.7128 1.0021590 ## trend[71,1] -2.672005e-01 -4.531257e-02 0.49513465 794.9446 1.0018889 ## trend[72,1] -2.385470e-01 -1.479362e-02 0.54417715 792.5568 1.0015851 ## trend[73,1] -2.018155e-01 2.821650e-02 0.59567437 795.6922 1.0012694 ## trend[74,1] -1.737040e-01 7.572632e-02 0.65111107 805.7620 1.0009668 ## trend[75,1] -1.392815e-01 1.180407e-01 0.70977420 823.3111 1.0007004 ## diag_SPD[1,1] 2.805380e+00 4.011913e+00 8.03758300 477.7263 1.0004637 ## diag_SPD[2,1] 2.738640e+00 3.760947e+00 6.34562875 576.0640 1.0001565 ## diag_SPD[3,1] 2.537465e+00 3.319090e+00 5.02219450 871.1366 1.0018018 ## diag_SPD[4,1] 2.249455e+00 2.875787e+00 4.39211375 1029.6020 1.0054388 ## diag_SPD[5,1] 2.003285e+00 2.574700e+00 3.81893050 731.8591 1.0079569 ## diag_SPD[6,1] 1.826065e+00 2.338935e+00 3.46473450 542.0990 1.0087476 ## diag_SPD[7,1] 1.673930e+00 2.121358e+00 3.19182525 461.1201 1.0085752 ## diag_SPD[8,1] 1.504910e+00 1.948352e+00 2.91990875 426.7440 1.0078665 ## diag_SPD[9,1] 1.359855e+00 1.787203e+00 2.68124300 407.9446 1.0068338 ## diag_SPD[10,1] 1.215155e+00 1.644900e+00 2.52324400 399.5770 1.0056384 ## diag_SPD[11,1] 1.074990e+00 1.507653e+00 2.37798050 399.7249 1.0044137 ## diag_SPD[12,1] 9.343420e-01 1.384760e+00 2.26188800 405.5516 1.0032596 ## diag_SPD[13,1] 7.915470e-01 1.271185e+00 2.15147775 415.3139 1.0022404 ## diag_SPD[14,1] 6.670285e-01 1.169145e+00 2.07266225 427.8118 1.0013902 ## diag_SPD[15,1] 5.493220e-01 1.056652e+00 1.98848475 442.1579 1.0007190 ## diag_SPD[16,1] 4.428535e-01 9.680762e-01 1.92180500 457.6779 1.0002205 ## diag_SPD[17,1] 3.542815e-01 8.788475e-01 1.83900900 473.8636 0.9998783 ## diag_SPD[18,1] 2.809345e-01 7.979983e-01 1.78158000 490.3433 0.9996709 ## diag_SPD[19,1] 2.187540e-01 7.092882e-01 1.70742125 506.8585 0.9995751 ## diag_SPD[20,1] 1.683520e-01 6.356428e-01 1.63541800 523.2421 0.9995685 ## SPD_beta[1,1] -3.159620e-01 1.487847e+00 6.86810325 714.4764 1.0036936 ## SPD_beta[2,1] 2.730900e+00 4.138687e+00 7.30706375 1124.0633 1.0010056 ## SPD_beta[3,1] 1.421515e+00 2.901905e+00 6.65818575 1074.9058 1.0013259 ## SPD_beta[4,1] -2.623540e+00 -1.536703e+00 1.05917050 1396.6907 1.0009804 ## SPD_beta[5,1] -1.299650e+00 -2.672713e-01 1.65368425 1346.1883 1.0027092 ## SPD_beta[6,1] 9.039160e-01 2.076275e+00 4.73776475 1302.8576 0.9997876 ## SPD_beta[7,1] 2.622880e-01 1.226322e+00 3.65493750 1549.8654 0.9998142 ## SPD_beta[8,1] 6.842440e-02 8.113705e-01 2.74523000 1550.2316 1.0013588 ## SPD_beta[9,1] 3.018150e-01 1.113600e+00 3.12365500 1748.8581 1.0000261 ## SPD_beta[10,1] -6.053590e-02 2.096683e-01 1.90656250 1712.3800 0.9998046 ## SPD_beta[11,1] -4.267395e-01 5.650525e-06 1.16964625 1274.0985 1.0010375 ## SPD_beta[12,1] -1.374745e-07 3.143380e-01 1.86855975 1931.2293 0.9999435 ## SPD_beta[13,1] 2.199965e-01 9.347765e-01 2.53515450 1354.5074 1.0025140 ## SPD_beta[14,1] 1.049195e-02 5.364973e-01 2.29640450 1864.6475 0.9996721 ## SPD_beta[15,1] -4.823565e-02 5.465603e-03 1.07355450 1646.9156 1.0012145 ## SPD_beta[16,1] -3.211785e-04 6.081203e-02 1.26472825 2496.9134 0.9991997 ## SPD_beta[17,1] 5.171120e-03 4.048033e-01 2.17579550 1498.1106 0.9995296 ## SPD_beta[18,1] 3.531165e-10 1.548950e-01 1.22768500 1922.0934 1.0021497 ## SPD_beta[19,1] -3.441460e-04 7.382327e-03 0.69703672 1477.2803 1.0005977 ## SPD_beta[20,1] -2.481185e-18 4.310163e-02 0.92760915 1834.0604 0.9995521 ## b[1] 1.010430e+00 1.217910e+00 1.79539650 749.8470 1.0031587 ## b[2] -3.530780e-01 -2.626075e-01 -0.07733668 1864.4436 0.9989885 ## b[3] -3.936525e-01 -2.822005e-01 -0.07272681 2196.2803 1.0015970 ## b[4] -1.568370e-01 -4.124093e-02 0.14849210 2162.3200 1.0004384 ## b[5] 1.585095e-01 2.488188e-01 0.42712142 2381.0109 1.0014187 ## b[6] 5.674360e-01 6.703220e-01 0.84482287 2456.5333 1.0001170 ## b[7] 3.922330e-01 4.902590e-01 0.67011445 2472.0645 1.0001199 ## mus[1,1] 1.624725e+00 1.805592e+00 2.09702750 1355.5494 0.9988460 ## mus[2,1] 1.423230e+00 1.570985e+00 1.84889450 1332.9277 0.9986383 ## mus[3,1] 1.304765e+00 1.449510e+00 1.72007350 1449.6059 0.9992687 ## mus[4,1] 1.315495e+00 1.472797e+00 1.75839775 1733.6681 1.0020683 ## mus[5,1] 1.468930e+00 1.602575e+00 1.83431725 2069.5362 1.0020176 ## mus[6,1] 1.655290e+00 1.779240e+00 2.01131275 2281.6765 1.0001367 ## mus[7,1] 1.854750e+00 1.972680e+00 2.18267850 2301.9058 0.9995416 ## mus[8,1] 2.153630e+00 2.253563e+00 2.45049400 2260.6663 1.0002967 ## mus[9,1] 2.355070e+00 2.455213e+00 2.67012225 1927.0591 1.0011336 ## mus[10,1] 2.248990e+00 2.364488e+00 2.57524500 1719.1099 1.0026739 ## mus[11,1] 1.983365e+00 2.098690e+00 2.30178400 1608.1193 1.0024670 ## mus[12,1] 1.677795e+00 1.793108e+00 2.01183000 1723.2020 1.0021084 ## mus[13,1] 1.645640e+00 1.758830e+00 1.99090750 1762.0681 1.0023048 ## mus[14,1] 1.367930e+00 1.497057e+00 1.74171450 1676.8760 1.0013748 ## mus[15,1] 1.183845e+00 1.331087e+00 1.59713500 1683.6427 0.9997472 ## mus[16,1] 1.120720e+00 1.281370e+00 1.55284650 1976.7522 0.9997404 ## mus[17,1] 1.188970e+00 1.337893e+00 1.59418375 1961.3585 0.9998653 ## mus[18,1] 1.297760e+00 1.440275e+00 1.68951075 1862.2932 1.0004594 ## mus[19,1] 1.423750e+00 1.553170e+00 1.78532125 1777.7877 1.0003404 ## mus[20,1] 1.651910e+00 1.779018e+00 1.99997900 1400.3200 0.9997495 ## mus[21,1] 1.799975e+00 1.928138e+00 2.18139075 1046.6830 0.9987424 ## mus[22,1] 1.647410e+00 1.793627e+00 2.02458100 918.1749 0.9993577 ## mus[23,1] 1.356650e+00 1.500698e+00 1.72810400 881.4249 0.9996759 ## mus[24,1] 1.031420e+00 1.187807e+00 1.44555125 925.9754 0.9995781 ## mus[25,1] 1.000004e+00 1.152268e+00 1.40838100 955.3135 0.9994870 ## mus[26,1] 7.482180e-01 8.974770e-01 1.15786350 1072.9949 0.9991625 ## mus[27,1] 5.977900e-01 7.506978e-01 1.02086125 1267.6168 0.9995088 ## mus[28,1] 5.773875e-01 7.338060e-01 1.00823875 1630.7730 1.0012350 ## mus[29,1] 7.016320e-01 8.413930e-01 1.10583625 1799.8941 1.0010344 ## mus[30,1] 8.703405e-01 1.006722e+00 1.28089000 2074.3049 0.9997322 ## mus[31,1] 1.066430e+00 1.200680e+00 1.46404375 2016.3592 0.9992676 ## mus[32,1] 1.358140e+00 1.487005e+00 1.75126350 1529.2684 1.0002198 ## mus[33,1] 1.566245e+00 1.707727e+00 1.97796750 1313.0470 1.0005325 ## mus[34,1] 1.475465e+00 1.616865e+00 1.91347200 1183.9184 1.0000687 ## mus[35,1] 1.212900e+00 1.381665e+00 1.66580875 983.4201 0.9995765 ## mus[36,1] 9.157430e-01 1.087955e+00 1.38147425 929.5306 1.0003829 ## mus[37,1] 8.826610e-01 1.057815e+00 1.36094375 927.6439 1.0004009 ## mus[38,1] 6.092715e-01 7.880942e-01 1.12985450 958.9882 1.0006665 ## mus[39,1] 4.328765e-01 6.031468e-01 0.95265270 1079.8237 0.9999583 ## mus[40,1] 3.644545e-01 5.512442e-01 0.88687003 1343.6257 1.0001640 ## mus[41,1] 4.183920e-01 5.912682e-01 0.91128560 1613.0600 1.0004717 ## mus[42,1] 5.210970e-01 6.818675e-01 0.99286630 1943.8662 1.0008517 ## mus[43,1] 6.472305e-01 8.008648e-01 1.09336125 2360.4966 1.0006362 ## mus[44,1] 8.779715e-01 1.022698e+00 1.28955950 2295.6338 1.0004762 ## mus[45,1] 1.025830e+00 1.175190e+00 1.42502200 1532.7972 1.0004016 ## mus[46,1] 8.736205e-01 1.031562e+00 1.28862675 1193.4454 1.0016516 ## mus[47,1] 5.763985e-01 7.362475e-01 1.02188925 1027.0579 1.0016575 ## mus[48,1] 2.512195e-01 4.276458e-01 0.73155652 1035.0487 1.0009472 ## mus[49,1] 2.244665e-01 4.058468e-01 0.70335472 1002.8483 1.0011813 ## mus[50,1] -3.072775e-02 1.537375e-01 0.46136797 1067.2708 1.0015643 ## mus[51,1] -1.792845e-01 1.085385e-02 0.33279485 1233.1994 1.0021547 ## mus[52,1] -1.762215e-01 1.615398e-02 0.34527242 1435.5715 1.0029660 ## mus[53,1] -3.964930e-02 1.449008e-01 0.46277495 1524.4083 1.0033428 ## mus[54,1] 1.399740e-01 3.125520e-01 0.63186112 1696.3914 1.0029888 ## mus[55,1] 3.512865e-01 5.151285e-01 0.80485085 2005.0651 1.0019876 ## mus[56,1] 6.691025e-01 8.290825e-01 1.10009100 2128.7445 1.0008711 ## mus[57,1] 9.068335e-01 1.071745e+00 1.35276075 2255.6564 1.0001190 ## mus[58,1] 8.468000e-01 1.005440e+00 1.30547550 2324.9764 1.0006387 ## mus[59,1] 6.292420e-01 7.807750e-01 1.06688800 2280.8030 1.0001559 ## mus[60,1] 3.817915e-01 5.270405e-01 0.82622770 2194.5528 0.9997073 ## mus[61,1] 4.063045e-01 5.537727e-01 0.86710535 2135.8702 0.9994967 ## mus[62,1] 1.972895e-01 3.551837e-01 0.69863225 1774.1706 0.9993230 ## mus[63,1] 9.072390e-02 2.644705e-01 0.60780265 1672.2157 0.9993997 ## mus[64,1] 1.096540e-01 2.924485e-01 0.64339037 1779.5908 1.0007050 ## mus[65,1] 2.573695e-01 4.401945e-01 0.74587437 1777.8822 1.0000127 ## mus[66,1] 4.638255e-01 6.295538e-01 0.92770185 2169.3004 0.9987117 ## mus[67,1] 6.843655e-01 8.381840e-01 1.12080675 2315.7624 0.9985545 ## mus[68,1] 9.977015e-01 1.146313e+00 1.42375525 2193.5436 0.9994294 ## mus[69,1] 1.229800e+00 1.382988e+00 1.65303225 2246.5959 0.9997798 ## mus[70,1] 1.176515e+00 1.325368e+00 1.59538675 2210.6327 0.9998446 ## mus[71,1] 9.630580e-01 1.110853e+00 1.38942300 1986.2990 0.9998859 ## mus[72,1] 7.176735e-01 8.742512e-01 1.14838500 1982.2133 1.0004448 ## mus[73,1] 7.478715e-01 9.208232e-01 1.21704525 2063.7219 1.0003372 ## mus[74,1] 5.489000e-01 7.373525e-01 1.07402725 2172.4920 0.9999074 ## mus[75,1] 4.372860e-01 6.541405e-01 1.08200400 2139.9592 0.9988735 ## rho[1] 3.653715e+00 3.944875e+00 4.38931575 1442.2886 1.0019543 ## ypred[1,1] 5.000000e+00 7.000000e+00 11.00000000 1250.3989 1.0015572 ## ypred[2,1] 4.000000e+00 6.000000e+00 9.00000000 2234.6005 0.9986285 ## ypred[3,1] 4.000000e+00 5.000000e+00 8.00000000 1938.0601 0.9987820 ## ypred[4,1] 4.000000e+00 5.000000e+00 9.00000000 1788.4118 1.0003975 ## ypred[5,1] 4.000000e+00 6.000000e+00 9.00000000 1977.2429 0.9989078 ## ypred[6,1] 5.000000e+00 7.000000e+00 11.00000000 1904.0206 0.9999394 ## ypred[7,1] 6.000000e+00 8.000000e+00 13.00000000 1970.3285 0.9994480 ## ypred[8,1] 8.000000e+00 1.100000e+01 16.00000000 1965.4290 0.9988468 ## ypred[9,1] 1.000000e+01 1.300000e+01 19.00000000 2031.8084 1.0029163 ## ypred[10,1] 9.000000e+00 1.200000e+01 18.00000000 1982.2104 1.0011334 ## ypred[11,1] 7.000000e+00 9.000000e+00 13.00000000 2112.8696 0.9988669 ## ypred[12,1] 5.000000e+00 7.000000e+00 11.00000000 1656.3924 1.0006936 ## ypred[13,1] 5.000000e+00 7.000000e+00 11.00000000 1829.8890 0.9982001 ## ypred[14,1] 4.000000e+00 5.000000e+00 9.00000000 1695.7919 1.0037188 ## ypred[15,1] 3.000000e+00 5.000000e+00 8.00000000 2040.4820 1.0010251 ## ypred[16,1] 3.000000e+00 4.000000e+00 7.00000000 1906.6704 1.0005641 ## ypred[17,1] 3.000000e+00 5.000000e+00 8.00000000 2078.9362 0.9990197 ## ypred[18,1] 4.000000e+00 5.000000e+00 8.00000000 2075.7098 0.9988486 ## ypred[19,1] 4.000000e+00 6.000000e+00 9.00000000 1922.3470 1.0000076 ## ypred[20,1] 5.000000e+00 7.000000e+00 10.00000000 1970.4054 0.9994512 ## ypred[21,1] 6.000000e+00 8.000000e+00 12.00000000 2051.3223 0.9990361 ## ypred[22,1] 5.000000e+00 7.000000e+00 11.00000000 1637.5878 1.0001885 ## ypred[23,1] 4.000000e+00 5.000000e+00 9.00000000 1695.0294 0.9987807 ## ypred[24,1] 3.000000e+00 4.000000e+00 7.00000000 1683.3550 1.0006054 ## ypred[25,1] 2.000000e+00 4.000000e+00 7.00000000 1826.6264 0.9999013 ## ypred[26,1] 2.000000e+00 3.000000e+00 6.00000000 1747.1677 0.9998833 ## ypred[27,1] 2.000000e+00 3.000000e+00 5.00000000 1849.8278 1.0010904 ## ypred[28,1] 2.000000e+00 3.000000e+00 5.00000000 2023.4120 0.9987513 ## ypred[29,1] 2.000000e+00 3.000000e+00 5.00000000 1995.6411 1.0000198 ## ypred[30,1] 2.000000e+00 3.000000e+00 6.00000000 1982.1083 1.0004518 ## ypred[31,1] 3.000000e+00 4.000000e+00 7.00000000 1800.7092 0.9987238 ## ypred[32,1] 4.000000e+00 5.000000e+00 8.00000000 1862.1536 0.9988347 ## ypred[33,1] 5.000000e+00 6.000000e+00 10.00000000 1912.2679 0.9996393 ## ypred[34,1] 4.000000e+00 6.000000e+00 10.00000000 1567.5015 0.9995528 ## ypred[35,1] 3.000000e+00 5.000000e+00 8.00000000 1666.4457 1.0005717 ## ypred[36,1] 2.000000e+00 4.000000e+00 6.00000000 1678.8776 0.9993531 ## ypred[37,1] 2.000000e+00 4.000000e+00 6.02500000 1821.0726 0.9991642 ## ypred[38,1] 2.000000e+00 3.000000e+00 5.00000000 1565.1870 0.9988901 ## ypred[39,1] 1.000000e+00 2.000000e+00 5.00000000 1954.0703 1.0012633 ## ypred[40,1] 1.000000e+00 2.000000e+00 4.00000000 1629.1795 1.0003239 ## ypred[41,1] 1.000000e+00 2.000000e+00 5.00000000 2167.9204 0.9991989 ## ypred[42,1] 1.000000e+00 3.000000e+00 5.00000000 1884.9395 1.0010027 ## ypred[43,1] 2.000000e+00 3.000000e+00 5.00000000 2049.6600 1.0001005 ## ypred[44,1] 2.000000e+00 3.000000e+00 6.00000000 1729.8587 1.0007607 ## ypred[45,1] 3.000000e+00 4.000000e+00 7.00000000 1904.6030 0.9989001 ## ypred[46,1] 2.000000e+00 3.000000e+00 6.00000000 1567.5881 1.0000772 ## ypred[47,1] 2.000000e+00 3.000000e+00 5.00000000 1900.7292 0.9991060 ## ypred[48,1] 1.000000e+00 2.000000e+00 4.00000000 1854.4138 0.9992814 ## ypred[49,1] 1.000000e+00 2.000000e+00 4.00000000 1882.9159 0.9995655 ## ypred[50,1] 1.000000e+00 2.000000e+00 3.00000000 1849.5721 1.0034080 ## ypred[51,1] 1.000000e+00 1.000000e+00 3.00000000 1652.6025 0.9997480 ## ypred[52,1] 1.000000e+00 1.000000e+00 3.00000000 2055.5882 1.0006921 ## ypred[53,1] 1.000000e+00 2.000000e+00 3.00000000 1787.7967 0.9988554 ## ypred[54,1] 1.000000e+00 2.000000e+00 4.00000000 1824.0332 0.9986548 ## ypred[55,1] 1.000000e+00 2.000000e+00 4.00000000 1772.4442 0.9998121 ## ypred[56,1] 2.000000e+00 3.000000e+00 5.00000000 2189.6816 1.0009768 ## ypred[57,1] 2.000000e+00 4.000000e+00 6.02500000 2130.6202 0.9985834 ## ypred[58,1] 2.000000e+00 3.000000e+00 6.00000000 2026.5377 0.9994474 ## ypred[59,1] 2.000000e+00 3.000000e+00 5.00000000 2161.5569 0.9996584 ## ypred[60,1] 1.000000e+00 2.000000e+00 4.00000000 2061.6866 1.0017438 ## ypred[61,1] 1.000000e+00 2.000000e+00 5.00000000 2039.8154 0.9998146 ## ypred[62,1] 1.000000e+00 2.000000e+00 4.00000000 2063.7861 0.9993196 ## ypred[63,1] 1.000000e+00 2.000000e+00 4.00000000 1865.2004 0.9995581 ## ypred[64,1] 1.000000e+00 2.000000e+00 4.00000000 1951.6409 0.9994485 ## ypred[65,1] 1.000000e+00 2.000000e+00 4.00000000 1703.0332 0.9993784 ## ypred[66,1] 1.000000e+00 2.000000e+00 5.00000000 1768.0996 0.9992407 ## ypred[67,1] 2.000000e+00 3.000000e+00 5.00000000 1695.6129 1.0001566 ## ypred[68,1] 3.000000e+00 4.000000e+00 7.00000000 2074.1567 0.9981473 ## ypred[69,1] 3.000000e+00 5.000000e+00 8.00000000 2149.4823 1.0001140 ## ypred[70,1] 3.000000e+00 5.000000e+00 8.00000000 1999.5596 0.9991075 ## ypred[71,1] 2.000000e+00 4.000000e+00 7.00000000 2125.5906 0.9993042 ## ypred[72,1] 2.000000e+00 3.000000e+00 5.02500000 2074.0179 0.9991322 ## ypred[73,1] 2.000000e+00 3.000000e+00 6.00000000 2001.4701 0.9998353 ## ypred[74,1] 2.000000e+00 3.000000e+00 5.00000000 1920.1687 0.9998691 ## ypred[75,1] 1.000000e+00 2.000000e+00 5.00000000 2046.6409 0.9988305 ## lp__ 6.780500e+01 7.083365e+01 75.45972000 491.5414 1.0089099 ## ## $c_summary ## , , chains = chain:1 ## ## stats ## parameter mean sd 2.5% 25% ## alpha_gp[1] 0.630676668 0.2049435 3.323511e-01 0.4720182500 ## rho_gp[1] 13.564870420 10.1703387 2.350519e+00 6.5019650000 ## b_gp[1,1] -0.068946832 0.9510737 -1.819025e+00 -0.7488205000 ## b_gp[2,1] 1.042210132 0.7960051 -4.318272e-01 0.4845017500 ## b_gp[3,1] 0.599442702 0.8316441 -1.118452e+00 0.0445108250 ## b_gp[4,1] -1.208637055 0.7584487 -2.646152e+00 -1.7047925000 ## b_gp[5,1] -0.605609004 0.7466967 -1.964010e+00 -1.1303625000 ## b_gp[6,1] 0.599241580 0.8274126 -8.998722e-01 0.0127264500 ## b_gp[7,1] 0.266562987 0.8557649 -1.450611e+00 -0.2615200000 ## b_gp[8,1] 0.106181413 0.8578888 -1.617424e+00 -0.4618615000 ## b_gp[9,1] 0.319654548 0.8506124 -1.215002e+00 -0.2461155000 ## b_gp[10,1] -0.211651186 0.8607377 -1.832723e+00 -0.7937662500 ## b_gp[11,1] -0.553696346 0.9544527 -2.311689e+00 -1.2526625000 ## b_gp[12,1] -0.020107472 0.8962962 -1.773567e+00 -0.6061740000 ## b_gp[13,1] 0.457060727 0.9468099 -1.574379e+00 -0.1355860000 ## b_gp[14,1] 0.218149695 0.8748198 -1.499041e+00 -0.3515107500 ## b_gp[15,1] -0.357224369 0.9022619 -2.096720e+00 -0.9745975000 ## b_gp[16,1] -0.153580439 0.9336034 -1.991205e+00 -0.7855487500 ## b_gp[17,1] 0.287064542 0.9803725 -1.442422e+00 -0.3745650000 ## b_gp[18,1] 0.081285530 0.9709677 -1.876265e+00 -0.5508355000 ## b_gp[19,1] -0.224379712 0.9098535 -1.906251e+00 -0.8131242500 ## b_gp[20,1] -0.089984953 0.9648841 -1.877308e+00 -0.7597462500 ## lambda[1] 40.314838580 17.6000404 1.137893e+01 26.7606750000 ## trend[1,1] 0.627013629 0.3536025 -8.285644e-02 0.4209025000 ## trend[2,1] 0.655874813 0.3471654 -1.326750e-02 0.4467120000 ## trend[3,1] 0.680979597 0.3441416 2.223780e-02 0.4574212500 ## trend[4,1] 0.702119494 0.3438542 2.779198e-02 0.4681650000 ## trend[5,1] 0.719060460 0.3455697 5.244765e-02 0.4829472500 ## trend[6,1] 0.731500768 0.3485886 4.037229e-02 0.4988270000 ## trend[7,1] 0.739047059 0.3523182 2.464656e-02 0.5122140000 ## trend[8,1] 0.741211386 0.3562982 1.696484e-02 0.5028142500 ## trend[9,1] 0.737431360 0.3601752 7.756224e-03 0.5067085000 ## trend[10,1] 0.727114850 0.3636444 -2.227277e-02 0.5068605000 ## trend[11,1] 0.709704285 0.3663907 -5.578628e-02 0.4875010000 ## trend[12,1] 0.684755611 0.3680675 -9.065494e-02 0.4746452500 ## trend[13,1] 0.652023351 0.3683383 -1.206433e-01 0.4352410000 ## trend[14,1] 0.611541477 0.3669720 -1.487511e-01 0.3890055000 ## trend[15,1] 0.563690199 0.3639673 -1.724903e-01 0.3359077500 ## trend[16,1] 0.509240040 0.3596547 -1.960223e-01 0.2807997500 ## trend[17,1] 0.449364134 0.3547196 -2.347707e-01 0.2207737500 ## trend[18,1] 0.385615293 0.3501062 -2.995778e-01 0.1673140000 ## trend[19,1] 0.319864252 0.3467832 -3.500613e-01 0.0997349500 ## trend[20,1] 0.254203157 0.3454286 -3.846647e-01 0.0313193750 ## trend[21,1] 0.190818952 0.3461549 -4.742128e-01 -0.0368934500 ## trend[22,1] 0.131846286 0.3484196 -5.143137e-01 -0.1040125000 ## trend[23,1] 0.079211408 0.3511907 -5.675813e-01 -0.1691082500 ## trend[24,1] 0.034480493 0.3533047 -6.175753e-01 -0.2088807500 ## trend[25,1] -0.001273561 0.3538805 -6.598018e-01 -0.2442297500 ## trend[26,1] -0.027574018 0.3526583 -6.679853e-01 -0.2689962500 ## trend[27,1] -0.044600907 0.3501815 -7.036386e-01 -0.2790167500 ## trend[28,1] -0.053203979 0.3477572 -7.374688e-01 -0.2857905000 ## trend[29,1] -0.054862312 0.3471519 -7.424221e-01 -0.2813872500 ## trend[30,1] -0.051594056 0.3500282 -7.599250e-01 -0.2749225000 ## trend[31,1] -0.045820293 0.3572836 -7.822184e-01 -0.2650847500 ## trend[32,1] -0.040193649 0.3686049 -8.264500e-01 -0.2598315000 ## trend[33,1] -0.037404404 0.3824899 -8.699770e-01 -0.2690447500 ## trend[34,1] -0.039979279 0.3966979 -9.098902e-01 -0.2868982500 ## trend[35,1] -0.050089305 0.4088542 -9.465622e-01 -0.2930650000 ## trend[36,1] -0.069381902 0.4169715 -9.782955e-01 -0.3195600000 ## trend[37,1] -0.098851357 0.4197920 -1.016016e+00 -0.3440640000 ## trend[38,1] -0.138758436 0.4169662 -1.048611e+00 -0.3768937500 ## trend[39,1] -0.188604890 0.4090962 -1.079667e+00 -0.4148032500 ## trend[40,1] -0.247165861 0.3976585 -1.108477e+00 -0.4548057500 ## trend[41,1] -0.312576671 0.3847891 -1.142244e+00 -0.5172432500 ## trend[42,1] -0.382467016 0.3728975 -1.176737e+00 -0.5866995000 ## trend[43,1] -0.454130808 0.3641160 -1.219187e+00 -0.6614167500 ## trend[44,1] -0.524719287 0.3597080 -1.252927e+00 -0.7109112500 ## trend[45,1] -0.591438781 0.3596921 -1.314065e+00 -0.8121030000 ## trend[46,1] -0.651740753 0.3629213 -1.378647e+00 -0.8720997500 ## trend[47,1] -0.703486490 0.3675793 -1.446566e+00 -0.9398920000 ## trend[48,1] -0.745075465 0.3718230 -1.476252e+00 -0.9840347500 ## trend[49,1] -0.775528477 0.3742946 -1.504885e+00 -1.0139750000 ## trend[50,1] -0.794519267 0.3743951 -1.529421e+00 -1.0387975000 ## trend[51,1] -0.802355568 0.3723275 -1.524273e+00 -1.0397225000 ## trend[52,1] -0.799912451 0.3689552 -1.522074e+00 -1.0323375000 ## trend[53,1] -0.788526733 0.3655161 -1.495472e+00 -1.0181625000 ## trend[54,1] -0.769860336 0.3632405 -1.482723e+00 -0.9967662500 ## trend[55,1] -0.745749048 0.3629727 -1.476321e+00 -0.9650310000 ## trend[56,1] -0.718047267 0.3649232 -1.470713e+00 -0.9283417500 ## trend[57,1] -0.688483229 0.3686554 -1.441131e+00 -0.9026305000 ## trend[58,1] -0.658536604 0.3732979 -1.423229e+00 -0.8877950000 ## trend[59,1] -0.629346267 0.3778662 -1.403415e+00 -0.8657240000 ## trend[60,1] -0.601655882 0.3815536 -1.366116e+00 -0.8424120000 ## trend[61,1] -0.575799119 0.3839035 -1.355718e+00 -0.7990700000 ## trend[62,1] -0.551723148 0.3848407 -1.349587e+00 -0.7799220000 ## trend[63,1] -0.529045280 0.3845911 -1.348474e+00 -0.7542930000 ## trend[64,1] -0.507137117 0.3835443 -1.347443e+00 -0.7417685000 ## trend[65,1] -0.485225941 0.3821152 -1.331883e+00 -0.7201242500 ## trend[66,1] -0.462502325 0.3806574 -1.293561e+00 -0.6994665000 ## trend[67,1] -0.438224870 0.3794519 -1.264724e+00 -0.6684865000 ## trend[68,1] -0.411811259 0.3787588 -1.223326e+00 -0.6249160000 ## trend[69,1] -0.382909475 0.3788892 -1.193171e+00 -0.5999475000 ## trend[70,1] -0.351441584 0.3802380 -1.145230e+00 -0.5654117500 ## trend[71,1] -0.317619099 0.3832409 -1.098984e+00 -0.5316787500 ## trend[72,1] -0.281929378 0.3882627 -1.070469e+00 -0.5111672500 ## trend[73,1] -0.245095116 0.3954627 -1.045408e+00 -0.5059950000 ## trend[74,1] -0.208012884 0.4047123 -9.915348e-01 -0.4664010000 ## trend[75,1] -0.171677411 0.4156171 -9.647892e-01 -0.4421385000 ## diag_SPD[1,1] 3.421934440 1.9612199 1.368178e+00 2.0372275000 ## diag_SPD[2,1] 3.102809360 1.4309198 1.361375e+00 2.0232050000 ## diag_SPD[3,1] 2.715034120 1.0239752 1.359228e+00 1.9542950000 ## diag_SPD[4,1] 2.348726270 0.8630522 1.076231e+00 1.7207775000 ## diag_SPD[5,1] 2.035759430 0.8259306 4.231070e-01 1.5176675000 ## diag_SPD[6,1] 1.775380924 0.8140156 1.207803e-01 1.3570225000 ## diag_SPD[7,1] 1.557933415 0.8001318 2.538488e-02 1.1014750000 ## diag_SPD[8,1] 1.374206927 0.7820647 4.319542e-03 0.8491272500 ## diag_SPD[9,1] 1.217290069 0.7614699 5.922637e-04 0.6011675000 ## diag_SPD[10,1] 1.082217234 0.7393874 6.533124e-05 0.3890175000 ## diag_SPD[11,1] 0.965317215 0.7162510 5.427901e-06 0.2566985000 ## diag_SPD[12,1] 0.863734725 0.6923678 3.559240e-07 0.1657005000 ## diag_SPD[13,1] 0.775156882 0.6680946 1.842177e-08 0.0981003250 ## diag_SPD[14,1] 0.697669156 0.6438160 7.526452e-10 0.0544740250 ## diag_SPD[15,1] 0.629672169 0.6198828 2.427591e-11 0.0281543750 ## diag_SPD[16,1] 0.569825598 0.5965701 6.181996e-13 0.0128069000 ## diag_SPD[17,1] 0.517003126 0.5740637 1.243078e-14 0.0061539675 ## diag_SPD[18,1] 0.470255514 0.5524684 1.973957e-16 0.0029335075 ## diag_SPD[19,1] 0.428779126 0.5318228 2.475697e-18 0.0013487550 ## diag_SPD[20,1] 0.391890661 0.5121192 2.452657e-20 0.0005957462 ## SPD_beta[1,1] -0.300651967 3.2256264 -7.070328e+00 -2.1630375000 ## SPD_beta[2,1] 2.879888113 2.1419099 -1.087817e+00 1.4285475000 ## SPD_beta[3,1] 1.715865241 2.6104395 -2.758343e+00 0.0940084500 ## SPD_beta[4,1] -2.615388145 1.8357371 -6.221184e+00 -3.6450050000 ## SPD_beta[5,1] -1.134113568 1.6629814 -4.297956e+00 -2.2461875000 ## SPD_beta[6,1] 1.087657418 1.6769037 -1.463901e+00 0.0138156750 ## SPD_beta[7,1] 0.512669947 1.3999150 -2.090424e+00 -0.2111462500 ## SPD_beta[8,1] 0.133744727 1.2447002 -2.434436e+00 -0.5194472500 ## SPD_beta[9,1] 0.519536392 1.1118870 -1.303465e+00 -0.0699635500 ## SPD_beta[10,1] -0.302337793 1.0939930 -2.699568e+00 -0.7830642500 ## SPD_beta[11,1] -0.638771548 1.1487250 -3.118336e+00 -1.1413525000 ## SPD_beta[12,1] -0.019283006 0.8557748 -1.901018e+00 -0.3688102500 ## SPD_beta[13,1] 0.430859570 0.8143793 -8.302909e-01 -0.0001669445 ## SPD_beta[14,1] 0.241784282 0.8254296 -1.252429e+00 -0.0379345500 ## SPD_beta[15,1] -0.277801407 0.7264338 -2.012842e+00 -0.5518050000 ## SPD_beta[16,1] -0.137384722 0.6569985 -1.611486e+00 -0.3651922500 ## SPD_beta[17,1] 0.259064125 0.6951955 -6.645827e-01 -0.0081178875 ## SPD_beta[18,1] 0.003190359 0.5318916 -1.385117e+00 -0.0674751000 ## SPD_beta[19,1] -0.202732264 0.5347603 -1.685835e+00 -0.3233862500 ## SPD_beta[20,1] -0.048649281 0.4363890 -1.247484e+00 -0.0926185750 ## b[1] 1.032991501 0.3319451 4.191766e-01 0.8081277500 ## b[2] -0.356570109 0.1423451 -6.756525e-01 -0.4465060000 ## b[3] -0.400773362 0.1651530 -7.511402e-01 -0.4991162500 ## b[4] -0.151093442 0.1571786 -4.535844e-01 -0.2625065000 ## b[5] 0.152293019 0.1368137 -1.289018e-01 0.0697962500 ## b[6] 0.562420932 0.1431835 2.850838e-01 0.4557022500 ## b[7] 0.389466400 0.1425345 1.002107e-01 0.2932332500 ## mus[1,1] 1.618977314 0.2783412 9.921207e-01 1.4501950000 ## mus[2,1] 1.416158764 0.2431705 8.904296e-01 1.2583025000 ## mus[3,1] 1.302263158 0.2228917 8.517674e-01 1.1578650000 ## mus[4,1] 1.314755544 0.2096270 9.083771e-01 1.1832725000 ## mus[5,1] 1.463159934 0.1838293 1.045494e+00 1.3440625000 ## mus[6,1] 1.653353140 0.1769360 1.305538e+00 1.5434850000 ## mus[7,1] 1.845233700 0.1601925 1.553222e+00 1.7360575000 ## mus[8,1] 2.133690840 0.1526969 1.822448e+00 2.0397550000 ## mus[9,1] 2.335867320 0.1605871 2.016862e+00 2.2278250000 ## mus[10,1] 2.237470100 0.1613987 1.904420e+00 2.1405100000 ## mus[11,1] 1.974968160 0.1575736 1.653781e+00 1.8688925000 ## mus[12,1] 1.676719660 0.1716345 1.329280e+00 1.5628275000 ## mus[13,1] 1.643987420 0.1733820 1.298163e+00 1.5343475000 ## mus[14,1] 1.371825352 0.1861161 1.033394e+00 1.2523600000 ## mus[15,1] 1.184974070 0.2041341 8.035201e-01 1.0494950000 ## mus[16,1] 1.121875938 0.2182683 7.316207e-01 0.9821452500 ## mus[17,1] 1.193463534 0.2052073 8.105592e-01 1.0424500000 ## mus[18,1] 1.307467922 0.2017494 9.422291e-01 1.1657050000 ## mus[19,1] 1.426051604 0.1894335 1.038850e+00 1.3097200000 ## mus[20,1] 1.646682440 0.1918434 1.230558e+00 1.5375975000 ## mus[21,1] 1.789254666 0.2125630 1.340539e+00 1.6663325000 ## mus[22,1] 1.642201756 0.2262052 1.150255e+00 1.4934850000 ## mus[23,1] 1.344475030 0.2323279 8.621128e-01 1.1944300000 ## mus[24,1] 1.026444399 0.2449669 5.249722e-01 0.8774385000 ## mus[25,1] 0.990690468 0.2484728 4.741747e-01 0.8333462500 ## mus[26,1] 0.732709965 0.2503488 1.966526e-01 0.5901225000 ## mus[27,1] 0.576682785 0.2503808 4.619733e-02 0.4147407500 ## mus[28,1] 0.559432073 0.2468099 2.765776e-02 0.4128467500 ## mus[29,1] 0.689237124 0.2234155 2.098706e-01 0.5527585000 ## mus[30,1] 0.870258468 0.2146112 4.405324e-01 0.7319707500 ## mus[31,1] 1.060366820 0.2077333 6.636645e-01 0.9285297500 ## mus[32,1] 1.352285608 0.2074293 9.293644e-01 1.2112450000 ## mus[33,1] 1.561031364 0.2150150 1.142173e+00 1.4171500000 ## mus[34,1] 1.470376076 0.2210693 1.026529e+00 1.3143100000 ## mus[35,1] 1.215174358 0.2297538 7.839337e-01 1.0584075000 ## mus[36,1] 0.922582156 0.2478743 4.681046e-01 0.7481185000 ## mus[37,1] 0.893112590 0.2503273 4.276076e-01 0.7185515000 ## mus[38,1] 0.621525475 0.2521224 1.312917e-01 0.4485015000 ## mus[39,1] 0.432678795 0.2582038 -8.588275e-02 0.2517050000 ## mus[40,1] 0.365470137 0.2636769 -1.546682e-01 0.1782855000 ## mus[41,1] 0.431522764 0.2414091 -5.024027e-02 0.2590947500 ## mus[42,1] 0.539385497 0.2310209 7.438657e-02 0.3865380000 ## mus[43,1] 0.652056134 0.2226185 1.876950e-01 0.5098870000 ## mus[44,1] 0.867760113 0.2231503 3.888122e-01 0.7298422500 ## mus[45,1] 1.006997154 0.2385853 4.665417e-01 0.8689217500 ## mus[46,1] 0.858614891 0.2564876 3.032403e-01 0.7030817500 ## mus[47,1] 0.561777416 0.2697822 -3.616045e-02 0.4030652500 ## mus[48,1] 0.246888493 0.2831086 -3.806901e-01 0.0849722000 ## mus[49,1] 0.216435412 0.2886835 -4.336353e-01 0.0399924500 ## mus[50,1] -0.034235402 0.2892554 -6.743053e-01 -0.2091075000 ## mus[51,1] -0.181071825 0.2925091 -7.748599e-01 -0.3546027500 ## mus[52,1] -0.187276443 0.2926152 -8.100596e-01 -0.3809437500 ## mus[53,1] -0.044427274 0.2698619 -6.191648e-01 -0.2034287500 ## mus[54,1] 0.151992107 0.2556050 -3.479437e-01 -0.0219055000 ## mus[55,1] 0.360437877 0.2391287 -1.291866e-01 0.2013217500 ## mus[56,1] 0.674432006 0.2322033 2.234489e-01 0.5307492500 ## mus[57,1] 0.909952491 0.2375836 4.459059e-01 0.7368332500 ## mus[58,1] 0.851818712 0.2357022 3.754774e-01 0.6929705000 ## mus[59,1] 0.635917582 0.2249949 1.812607e-01 0.4808025000 ## mus[60,1] 0.390308116 0.2264283 -5.717305e-02 0.2346002500 ## mus[61,1] 0.416164774 0.2279821 -3.859789e-02 0.2669795000 ## mus[62,1] 0.208560709 0.2356750 -2.421512e-01 0.0507890750 ## mus[63,1] 0.092238428 0.2506357 -3.662038e-01 -0.0757589000 ## mus[64,1] 0.105498929 0.2625177 -4.342735e-01 -0.0707585250 ## mus[65,1] 0.258873495 0.2485267 -2.595255e-01 0.0904366250 ## mus[66,1] 0.459350076 0.2438991 -5.606533e-02 0.3000515000 ## mus[67,1] 0.667962070 0.2374197 2.000165e-01 0.5042695000 ## mus[68,1] 0.980667962 0.2282878 5.548555e-01 0.8186292500 ## mus[69,1] 1.215526184 0.2265350 8.009234e-01 1.0564425000 ## mus[70,1] 1.158913910 0.2322631 7.064530e-01 0.9963622500 ## mus[71,1] 0.947644576 0.2326583 4.677982e-01 0.7830460000 ## mus[72,1] 0.710034663 0.2375571 2.222688e-01 0.5522547500 ## mus[73,1] 0.746868922 0.2490844 2.415246e-01 0.5785975000 ## mus[74,1] 0.552271032 0.2720101 -1.354676e-02 0.3799210000 ## mus[75,1] 0.449606211 0.3130215 -1.782414e-01 0.2322617500 ## rho[1] 3.589572620 0.4890731 2.431573e+00 3.2869375000 ## ypred[1,1] 5.014000000 2.5602566 1.000000e+00 3.0000000000 ## ypred[2,1] 4.232000000 2.2822343 4.750000e-01 3.0000000000 ## ypred[3,1] 3.778000000 2.1065591 0.000000e+00 2.0000000000 ## ypred[4,1] 3.770000000 2.0092721 1.000000e+00 2.0000000000 ## ypred[5,1] 4.480000000 2.3281840 1.000000e+00 3.0000000000 ## ypred[6,1] 5.164000000 2.4910871 1.000000e+00 3.0000000000 ## ypred[7,1] 6.518000000 2.7736370 2.000000e+00 4.0000000000 ## ypred[8,1] 8.700000000 3.2445422 3.000000e+00 6.0000000000 ## ypred[9,1] 10.328000000 3.4572128 4.000000e+00 8.0000000000 ## ypred[10,1] 9.482000000 3.5302410 3.000000e+00 7.0000000000 ## ypred[11,1] 7.260000000 2.8950237 2.475000e+00 5.0000000000 ## ypred[12,1] 5.378000000 2.5534597 1.000000e+00 3.7500000000 ## ypred[13,1] 5.260000000 2.6080652 1.000000e+00 3.0000000000 ## ypred[14,1] 3.962000000 2.1367469 1.000000e+00 3.0000000000 ## ypred[15,1] 3.242000000 2.0957625 0.000000e+00 2.0000000000 ## ypred[16,1] 3.028000000 1.8874164 0.000000e+00 2.0000000000 ## ypred[17,1] 3.462000000 2.0021421 0.000000e+00 2.0000000000 ## ypred[18,1] 3.814000000 2.1635077 0.000000e+00 2.0000000000 ## ypred[19,1] 4.402000000 2.3322252 1.000000e+00 3.0000000000 ## ypred[20,1] 5.132000000 2.4945986 1.000000e+00 3.0000000000 ## ypred[21,1] 6.208000000 2.8909256 2.000000e+00 4.0000000000 ## ypred[22,1] 5.270000000 2.6219935 1.000000e+00 3.0000000000 ## ypred[23,1] 3.838000000 2.0939258 1.000000e+00 2.0000000000 ## ypred[24,1] 2.870000000 1.8611900 0.000000e+00 2.0000000000 ## ypred[25,1] 2.772000000 1.8073597 0.000000e+00 1.0000000000 ## ypred[26,1] 2.130000000 1.4877927 0.000000e+00 1.0000000000 ## ypred[27,1] 1.838000000 1.4112900 0.000000e+00 1.0000000000 ## ypred[28,1] 1.778000000 1.3683789 0.000000e+00 1.0000000000 ## ypred[29,1] 2.034000000 1.5157305 0.000000e+00 1.0000000000 ## ypred[30,1] 2.566000000 1.7342605 0.000000e+00 1.0000000000 ## ypred[31,1] 2.970000000 1.8449682 0.000000e+00 2.0000000000 ## ypred[32,1] 3.988000000 2.2463187 1.000000e+00 2.0000000000 ## ypred[33,1] 4.800000000 2.3381475 1.000000e+00 3.0000000000 ## ypred[34,1] 4.608000000 2.4070571 1.000000e+00 3.0000000000 ## ypred[35,1] 3.616000000 2.1311094 0.000000e+00 2.0000000000 ## ypred[36,1] 2.460000000 1.6290204 0.000000e+00 1.0000000000 ## ypred[37,1] 2.610000000 1.6910409 0.000000e+00 1.0000000000 ## ypred[38,1] 1.918000000 1.4790711 0.000000e+00 1.0000000000 ## ypred[39,1] 1.606000000 1.2985131 0.000000e+00 1.0000000000 ## ypred[40,1] 1.536000000 1.3115427 0.000000e+00 1.0000000000 ## ypred[41,1] 1.644000000 1.3464360 0.000000e+00 1.0000000000 ## ypred[42,1] 1.742000000 1.4054845 0.000000e+00 1.0000000000 ## ypred[43,1] 1.934000000 1.5435054 0.000000e+00 1.0000000000 ## ypred[44,1] 2.370000000 1.6765206 0.000000e+00 1.0000000000 ## ypred[45,1] 2.868000000 1.7414480 0.000000e+00 2.0000000000 ## ypred[46,1] 2.286000000 1.6460933 0.000000e+00 1.0000000000 ## ypred[47,1] 1.906000000 1.5588534 0.000000e+00 1.0000000000 ## ypred[48,1] 1.286000000 1.2293195 0.000000e+00 0.0000000000 ## ypred[49,1] 1.320000000 1.1833853 0.000000e+00 0.0000000000 ## ypred[50,1] 0.954000000 1.0089201 0.000000e+00 0.0000000000 ## ypred[51,1] 0.842000000 0.9627512 0.000000e+00 0.0000000000 ## ypred[52,1] 0.832000000 0.9367663 0.000000e+00 0.0000000000 ## ypred[53,1] 0.934000000 0.9734162 0.000000e+00 0.0000000000 ## ypred[54,1] 1.160000000 1.1597802 0.000000e+00 0.0000000000 ## ypred[55,1] 1.456000000 1.2210840 0.000000e+00 0.0000000000 ## ypred[56,1] 2.076000000 1.5436936 0.000000e+00 1.0000000000 ## ypred[57,1] 2.450000000 1.7336410 0.000000e+00 1.0000000000 ## ypred[58,1] 2.354000000 1.6315661 0.000000e+00 1.0000000000 ## ypred[59,1] 2.022000000 1.5499421 0.000000e+00 1.0000000000 ## ypred[60,1] 1.560000000 1.2655446 0.000000e+00 1.0000000000 ## ypred[61,1] 1.554000000 1.2578746 0.000000e+00 1.0000000000 ## ypred[62,1] 1.238000000 1.1206550 0.000000e+00 0.0000000000 ## ypred[63,1] 1.076000000 1.0791446 0.000000e+00 0.0000000000 ## ypred[64,1] 1.068000000 1.0925949 0.000000e+00 0.0000000000 ## ypred[65,1] 1.332000000 1.1969299 0.000000e+00 0.0000000000 ## ypred[66,1] 1.574000000 1.3726954 0.000000e+00 0.0000000000 ## ypred[67,1] 1.972000000 1.4336410 0.000000e+00 1.0000000000 ## ypred[68,1] 2.726000000 1.7712138 0.000000e+00 1.0000000000 ## ypred[69,1] 3.372000000 1.9762153 0.000000e+00 2.0000000000 ## ypred[70,1] 3.340000000 1.9596122 0.000000e+00 2.0000000000 ## ypred[71,1] 2.720000000 1.6586447 0.000000e+00 1.0000000000 ## ypred[72,1] 2.098000000 1.5714117 0.000000e+00 1.0000000000 ## ypred[73,1] 2.230000000 1.6069426 0.000000e+00 1.0000000000 ## ypred[74,1] 1.826000000 1.4155322 0.000000e+00 1.0000000000 ## ypred[75,1] 1.610000000 1.3496455 0.000000e+00 1.0000000000 ## lp__ 67.486116800 4.4633491 5.803434e+01 64.3417000000 ## stats ## parameter 50% 75% 97.5% ## alpha_gp[1] 5.989920e-01 0.7456917500 1.112038750 ## rho_gp[1] 1.029955e+01 17.3836500000 40.508125000 ## b_gp[1,1] -1.392890e-01 0.5758785000 1.828837750 ## b_gp[2,1] 9.928175e-01 1.5543675000 2.614150750 ## b_gp[3,1] 6.523545e-01 1.1751900000 2.133696500 ## b_gp[4,1] -1.213025e+00 -0.6509982500 0.241499175 ## b_gp[5,1] -6.251910e-01 -0.1299895000 0.866344500 ## b_gp[6,1] 5.912540e-01 1.1641300000 2.234196750 ## b_gp[7,1] 2.818890e-01 0.8079517500 1.907626750 ## b_gp[8,1] 1.150130e-01 0.6228517500 1.933322750 ## b_gp[9,1] 3.065860e-01 0.8981427500 2.070926500 ## b_gp[10,1] -2.378635e-01 0.4081250000 1.367780000 ## b_gp[11,1] -5.774505e-01 0.0751935500 1.307796500 ## b_gp[12,1] 2.076120e-03 0.5404210000 1.706026750 ## b_gp[13,1] 5.272255e-01 1.0217550000 2.179095000 ## b_gp[14,1] 1.745690e-01 0.8079912500 1.943642000 ## b_gp[15,1] -3.797160e-01 0.2569240000 1.460732000 ## b_gp[16,1] -1.541175e-01 0.4385177500 1.743525250 ## b_gp[17,1] 3.146595e-01 0.8920015000 2.300468250 ## b_gp[18,1] 5.482945e-02 0.6877430000 2.062689250 ## b_gp[19,1] -2.043555e-01 0.3506727500 1.494673500 ## b_gp[20,1] -1.146150e-01 0.5081440000 1.714571250 ## lambda[1] 3.941720e+01 51.4274750000 77.682735000 ## trend[1,1] 6.227650e-01 0.8438142500 1.340511500 ## trend[2,1] 6.550530e-01 0.8653042500 1.386201750 ## trend[3,1] 6.815270e-01 0.8947657500 1.366915500 ## trend[4,1] 7.079865e-01 0.9282747500 1.384180250 ## trend[5,1] 7.336355e-01 0.9457287500 1.425266250 ## trend[6,1] 7.405830e-01 0.9659212500 1.446570750 ## trend[7,1] 7.435780e-01 0.9688877500 1.432003750 ## trend[8,1] 7.479870e-01 0.9711300000 1.436606000 ## trend[9,1] 7.412625e-01 0.9635977500 1.419953500 ## trend[10,1] 7.372025e-01 0.9564645000 1.417418750 ## trend[11,1] 7.235345e-01 0.9515500000 1.400116750 ## trend[12,1] 6.976410e-01 0.9353877500 1.387786500 ## trend[13,1] 6.610240e-01 0.8995640000 1.342800750 ## trend[14,1] 6.145460e-01 0.8525685000 1.272995750 ## trend[15,1] 5.626665e-01 0.7881477500 1.235978500 ## trend[16,1] 5.124975e-01 0.7376550000 1.194382000 ## trend[17,1] 4.579500e-01 0.6721075000 1.147024000 ## trend[18,1] 3.848955e-01 0.5988790000 1.071339750 ## trend[19,1] 3.232895e-01 0.5350260000 0.996033175 ## trend[20,1] 2.459395e-01 0.4731880000 0.949836275 ## trend[21,1] 1.891225e-01 0.4129490000 0.896973825 ## trend[22,1] 1.222895e-01 0.3691492500 0.828735325 ## trend[23,1] 5.822195e-02 0.3189850000 0.794334300 ## trend[24,1] 2.161530e-02 0.2839247500 0.749842250 ## trend[25,1] -6.208840e-03 0.2485380000 0.702870300 ## trend[26,1] -3.264010e-02 0.2259665000 0.671115025 ## trend[27,1] -4.347320e-02 0.2124805000 0.669204225 ## trend[28,1] -6.221325e-02 0.1844395000 0.648765600 ## trend[29,1] -5.407430e-02 0.1839682500 0.634311850 ## trend[30,1] -4.440210e-02 0.1797465000 0.635803550 ## trend[31,1] -3.112680e-02 0.1892972500 0.627154225 ## trend[32,1] -2.625105e-02 0.1936120000 0.651830100 ## trend[33,1] -1.853435e-02 0.1994262500 0.652025575 ## trend[34,1] -1.676270e-02 0.2194627500 0.677691875 ## trend[35,1] -2.395830e-02 0.2164995000 0.698872925 ## trend[36,1] -3.441660e-02 0.1875262500 0.697695125 ## trend[37,1] -8.067500e-02 0.1650210000 0.684403975 ## trend[38,1] -1.201860e-01 0.1205352500 0.649698450 ## trend[39,1] -1.782670e-01 0.0624178000 0.583479500 ## trend[40,1] -2.384150e-01 0.0004107805 0.481660550 ## trend[41,1] -2.892255e-01 -0.0577539500 0.370390850 ## trend[42,1] -3.645175e-01 -0.1242235000 0.317131775 ## trend[43,1] -4.224140e-01 -0.2157772500 0.247990950 ## trend[44,1] -4.946225e-01 -0.3003475000 0.163615325 ## trend[45,1] -5.621270e-01 -0.3566547500 0.114095575 ## trend[46,1] -6.206190e-01 -0.4050905000 0.048965035 ## trend[47,1] -6.807965e-01 -0.4713042500 0.007997361 ## trend[48,1] -7.175245e-01 -0.5039335000 -0.024411948 ## trend[49,1] -7.461725e-01 -0.5322867500 -0.074011383 ## trend[50,1] -7.678285e-01 -0.5555475000 -0.096101495 ## trend[51,1] -7.773875e-01 -0.5521532500 -0.106524075 ## trend[52,1] -7.732900e-01 -0.5628057500 -0.124408275 ## trend[53,1] -7.631205e-01 -0.5389812500 -0.123424975 ## trend[54,1] -7.407240e-01 -0.5189755000 -0.100652808 ## trend[55,1] -7.233120e-01 -0.4916417500 -0.069619500 ## trend[56,1] -7.000170e-01 -0.4696877500 -0.053405663 ## trend[57,1] -6.708560e-01 -0.4457415000 -0.015259043 ## trend[58,1] -6.384160e-01 -0.4208177500 0.049277212 ## trend[59,1] -6.135255e-01 -0.3929662500 0.085012415 ## trend[60,1] -5.776745e-01 -0.3650712500 0.138110375 ## trend[61,1] -5.564770e-01 -0.3253942500 0.159775000 ## trend[62,1] -5.307355e-01 -0.3043922500 0.189273825 ## trend[63,1] -5.108820e-01 -0.2712085000 0.221086950 ## trend[64,1] -4.906060e-01 -0.2574800000 0.260939025 ## trend[65,1] -4.679830e-01 -0.2329052500 0.273121250 ## trend[66,1] -4.386450e-01 -0.2125812500 0.262212000 ## trend[67,1] -4.190110e-01 -0.1833780000 0.278483600 ## trend[68,1] -3.880955e-01 -0.1527017500 0.298582625 ## trend[69,1] -3.602665e-01 -0.1288152500 0.342809525 ## trend[70,1] -3.203210e-01 -0.0886804750 0.392916700 ## trend[71,1] -2.886635e-01 -0.0636622500 0.414427850 ## trend[72,1] -2.527620e-01 -0.0229801250 0.484605425 ## trend[73,1] -2.159120e-01 0.0144706750 0.563805750 ## trend[74,1] -1.749810e-01 0.0517950750 0.606925075 ## trend[75,1] -1.454445e-01 0.0991005000 0.611178275 ## diag_SPD[1,1] 2.910680e+00 4.0656275000 8.795607500 ## diag_SPD[2,1] 2.809710e+00 3.7981025000 6.701704750 ## diag_SPD[3,1] 2.508500e+00 3.3040500000 5.034899750 ## diag_SPD[4,1] 2.172840e+00 2.8533800000 4.350170750 ## diag_SPD[5,1] 1.938915e+00 2.5179075000 3.792737250 ## diag_SPD[6,1] 1.750595e+00 2.2752550000 3.353602500 ## diag_SPD[7,1] 1.585170e+00 2.0662500000 3.008917750 ## diag_SPD[8,1] 1.431110e+00 1.8965475000 2.836168750 ## diag_SPD[9,1] 1.317280e+00 1.7600950000 2.625761750 ## diag_SPD[10,1] 1.148445e+00 1.6223525000 2.464925250 ## diag_SPD[11,1] 1.003655e+00 1.4875225000 2.360956750 ## diag_SPD[12,1] 8.706590e-01 1.3932100000 2.243019000 ## diag_SPD[13,1] 7.188865e-01 1.2694500000 2.147695750 ## diag_SPD[14,1] 5.937925e-01 1.1914525000 2.069051750 ## diag_SPD[15,1] 4.695835e-01 1.1094975000 1.976815750 ## diag_SPD[16,1] 3.906020e-01 1.0183975000 1.928281500 ## diag_SPD[17,1] 3.213690e-01 0.9209590000 1.830543500 ## diag_SPD[18,1] 2.527735e-01 0.8433330000 1.779828000 ## diag_SPD[19,1] 1.975275e-01 0.7513280000 1.733574250 ## diag_SPD[20,1] 1.511630e-01 0.6670840000 1.649139250 ## SPD_beta[1,1] -4.305800e-01 1.6531850000 6.336355000 ## SPD_beta[2,1] 2.771240e+00 4.3346975000 7.108284750 ## SPD_beta[3,1] 1.509080e+00 3.1006125000 6.746959750 ## SPD_beta[4,1] -2.580190e+00 -1.4979200000 0.815049750 ## SPD_beta[5,1] -1.084935e+00 -0.1658775000 1.911595500 ## SPD_beta[6,1] 8.495435e-01 2.0327700000 4.697829500 ## SPD_beta[7,1] 2.991065e-01 1.2216975000 3.853041000 ## SPD_beta[8,1] 6.179880e-02 0.7238890000 2.614526250 ## SPD_beta[9,1] 2.297700e-01 1.0768000000 3.092172000 ## SPD_beta[10,1] -7.419460e-02 0.1584200000 1.719576000 ## SPD_beta[11,1] -3.582605e-01 0.0002185685 1.240966750 ## SPD_beta[12,1] 7.087488e-09 0.3122567500 1.706061000 ## SPD_beta[13,1] 1.608445e-01 0.8922495000 2.436276500 ## SPD_beta[14,1] 2.184100e-03 0.4774670000 2.292052250 ## SPD_beta[15,1] -3.182595e-02 0.0017523775 1.044507750 ## SPD_beta[16,1] -9.909335e-05 0.0236655000 1.203844750 ## SPD_beta[17,1] 2.159960e-04 0.4042857500 2.007376750 ## SPD_beta[18,1] 8.270875e-15 0.1170280000 1.112270500 ## SPD_beta[19,1] -3.618795e-04 0.0004117470 0.566690950 ## SPD_beta[20,1] -1.432552e-15 0.0390723000 0.859185125 ## b[1] 1.024040e+00 1.2311700000 1.733057750 ## b[2] -3.527510e-01 -0.2664060000 -0.072335330 ## b[3] -3.970410e-01 -0.2978365000 -0.070945010 ## b[4] -1.401685e-01 -0.0401159500 0.139269225 ## b[5] 1.549340e-01 0.2391342500 0.434448100 ## b[6] 5.615060e-01 0.6755762500 0.833052450 ## b[7] 3.895760e-01 0.4875220000 0.669726825 ## mus[1,1] 1.643345e+00 1.8235950000 2.109844250 ## mus[2,1] 1.425570e+00 1.5898850000 1.858376500 ## mus[3,1] 1.299935e+00 1.4518500000 1.728233500 ## mus[4,1] 1.308040e+00 1.4666425000 1.704109750 ## mus[5,1] 1.470510e+00 1.5879950000 1.805170500 ## mus[6,1] 1.649435e+00 1.7746700000 1.973408250 ## mus[7,1] 1.843930e+00 1.9652925000 2.160418750 ## mus[8,1] 2.144705e+00 2.2333700000 2.422094250 ## mus[9,1] 2.342670e+00 2.4431775000 2.630386750 ## mus[10,1] 2.232065e+00 2.3371625000 2.563565500 ## mus[11,1] 1.961150e+00 2.0862975000 2.293336250 ## mus[12,1] 1.673320e+00 1.7942525000 2.022636500 ## mus[13,1] 1.641545e+00 1.7614700000 2.000305000 ## mus[14,1] 1.366350e+00 1.4885625000 1.761600500 ## mus[15,1] 1.180515e+00 1.3154425000 1.610926000 ## mus[16,1] 1.106995e+00 1.2639400000 1.562498750 ## mus[17,1] 1.198910e+00 1.3317350000 1.594258750 ## mus[18,1] 1.300295e+00 1.4469925000 1.679278500 ## mus[19,1] 1.422635e+00 1.5525275000 1.784475250 ## mus[20,1] 1.665370e+00 1.7845900000 1.968280500 ## mus[21,1] 1.812320e+00 1.9363700000 2.175731250 ## mus[22,1] 1.655480e+00 1.8076750000 2.004816750 ## mus[23,1] 1.364210e+00 1.5066350000 1.729332250 ## mus[24,1] 1.044420e+00 1.1959475000 1.460448250 ## mus[25,1] 1.005300e+00 1.1655775000 1.430636000 ## mus[26,1] 7.641345e-01 0.9129000000 1.154353750 ## mus[27,1] 5.975565e-01 0.7498440000 0.997345375 ## mus[28,1] 5.582550e-01 0.7282185000 1.025746750 ## mus[29,1] 6.963205e-01 0.8369080000 1.098577000 ## mus[30,1] 8.618955e-01 1.0037875000 1.303517000 ## mus[31,1] 1.046440e+00 1.1921800000 1.515907250 ## mus[32,1] 1.352770e+00 1.4805050000 1.781712750 ## mus[33,1] 1.558715e+00 1.6989550000 1.982534000 ## mus[34,1] 1.476825e+00 1.6046950000 1.906139750 ## mus[35,1] 1.209940e+00 1.3762575000 1.695282500 ## mus[36,1] 9.280470e-01 1.0935825000 1.379839750 ## mus[37,1] 8.941260e-01 1.0620750000 1.356414000 ## mus[38,1] 6.100380e-01 0.7904912500 1.136795000 ## mus[39,1] 4.344710e-01 0.6068817500 0.933793250 ## mus[40,1] 3.616585e-01 0.5567700000 0.882860375 ## mus[41,1] 4.271145e-01 0.6013230000 0.915335675 ## mus[42,1] 5.278720e-01 0.7016217500 0.984153125 ## mus[43,1] 6.521210e-01 0.8055397500 1.070950750 ## mus[44,1] 8.889270e-01 1.0256575000 1.244909750 ## mus[45,1] 1.028305e+00 1.1705175000 1.395779250 ## mus[46,1] 8.786815e-01 1.0330100000 1.290340750 ## mus[47,1] 5.907975e-01 0.7467957500 1.033503500 ## mus[48,1] 2.602915e-01 0.4487027500 0.748395025 ## mus[49,1] 2.341595e-01 0.4243512500 0.728047525 ## mus[50,1] -6.750260e-03 0.1629690000 0.488375675 ## mus[51,1] -1.589720e-01 0.0089499475 0.324316775 ## mus[52,1] -1.666420e-01 0.0160987250 0.318534875 ## mus[53,1] -1.713205e-02 0.1507462500 0.453836400 ## mus[54,1] 1.591255e-01 0.3274570000 0.629358675 ## mus[55,1] 3.556020e-01 0.5257507500 0.794392700 ## mus[56,1] 6.861970e-01 0.8423207500 1.089114250 ## mus[57,1] 9.201240e-01 1.0859925000 1.350940250 ## mus[58,1] 8.585170e-01 0.9974412500 1.274554750 ## mus[59,1] 6.331520e-01 0.7887207500 1.069683500 ## mus[60,1] 3.922390e-01 0.5515517500 0.809038800 ## mus[61,1] 4.156220e-01 0.5646745000 0.844873950 ## mus[62,1] 1.980175e-01 0.3574092500 0.667467425 ## mus[63,1] 7.655315e-02 0.2635255000 0.605135100 ## mus[64,1] 9.526275e-02 0.2853030000 0.619125600 ## mus[65,1] 2.634595e-01 0.4210882500 0.733121050 ## mus[66,1] 4.573975e-01 0.6264132500 0.905407550 ## mus[67,1] 6.681665e-01 0.8301665000 1.109881750 ## mus[68,1] 9.754240e-01 1.1416575000 1.423689250 ## mus[69,1] 1.217500e+00 1.3710775000 1.674395000 ## mus[70,1] 1.170890e+00 1.3162550000 1.586547250 ## mus[71,1] 9.635625e-01 1.1033700000 1.383428750 ## mus[72,1] 7.186195e-01 0.8728170000 1.149639250 ## mus[73,1] 7.498720e-01 0.9225292500 1.217259000 ## mus[74,1] 5.439755e-01 0.7426745000 1.091697500 ## mus[75,1] 4.484810e-01 0.6512167500 1.112355500 ## rho[1] 3.674200e+00 3.9401725000 4.352621000 ## ypred[1,1] 5.000000e+00 6.0000000000 11.000000000 ## ypred[2,1] 4.000000e+00 6.0000000000 9.000000000 ## ypred[3,1] 4.000000e+00 5.0000000000 8.000000000 ## ypred[4,1] 4.000000e+00 5.0000000000 8.000000000 ## ypred[5,1] 4.000000e+00 6.0000000000 9.000000000 ## ypred[6,1] 5.000000e+00 7.0000000000 10.000000000 ## ypred[7,1] 6.000000e+00 8.0000000000 12.000000000 ## ypred[8,1] 9.000000e+00 11.0000000000 15.000000000 ## ypred[9,1] 1.000000e+01 12.0000000000 17.525000000 ## ypred[10,1] 9.000000e+00 12.0000000000 17.525000000 ## ypred[11,1] 7.000000e+00 9.0000000000 13.000000000 ## ypred[12,1] 5.000000e+00 7.0000000000 11.000000000 ## ypred[13,1] 5.000000e+00 7.0000000000 11.000000000 ## ypred[14,1] 4.000000e+00 5.0000000000 9.000000000 ## ypred[15,1] 3.000000e+00 4.0000000000 8.000000000 ## ypred[16,1] 3.000000e+00 4.0000000000 7.000000000 ## ypred[17,1] 3.000000e+00 5.0000000000 8.000000000 ## ypred[18,1] 4.000000e+00 5.0000000000 9.000000000 ## ypred[19,1] 4.000000e+00 6.0000000000 10.000000000 ## ypred[20,1] 5.000000e+00 7.0000000000 10.525000000 ## ypred[21,1] 6.000000e+00 8.0000000000 13.000000000 ## ypred[22,1] 5.000000e+00 7.0000000000 11.000000000 ## ypred[23,1] 4.000000e+00 5.0000000000 8.525000000 ## ypred[24,1] 3.000000e+00 4.0000000000 7.000000000 ## ypred[25,1] 3.000000e+00 4.0000000000 7.000000000 ## ypred[26,1] 2.000000e+00 3.0000000000 5.000000000 ## ypred[27,1] 2.000000e+00 3.0000000000 5.000000000 ## ypred[28,1] 2.000000e+00 3.0000000000 5.000000000 ## ypred[29,1] 2.000000e+00 3.0000000000 6.000000000 ## ypred[30,1] 2.000000e+00 4.0000000000 6.525000000 ## ypred[31,1] 3.000000e+00 4.0000000000 7.000000000 ## ypred[32,1] 4.000000e+00 5.0000000000 9.000000000 ## ypred[33,1] 5.000000e+00 6.0000000000 10.000000000 ## ypred[34,1] 4.000000e+00 6.0000000000 10.000000000 ## ypred[35,1] 3.000000e+00 5.0000000000 8.525000000 ## ypred[36,1] 2.000000e+00 4.0000000000 6.000000000 ## ypred[37,1] 2.000000e+00 4.0000000000 6.000000000 ## ypred[38,1] 2.000000e+00 3.0000000000 5.000000000 ## ypred[39,1] 1.000000e+00 2.0000000000 5.000000000 ## ypred[40,1] 1.000000e+00 2.0000000000 4.000000000 ## ypred[41,1] 2.000000e+00 2.0000000000 5.000000000 ## ypred[42,1] 1.000000e+00 3.0000000000 5.000000000 ## ypred[43,1] 2.000000e+00 3.0000000000 5.525000000 ## ypred[44,1] 2.000000e+00 3.0000000000 6.000000000 ## ypred[45,1] 3.000000e+00 4.0000000000 7.000000000 ## ypred[46,1] 2.000000e+00 3.0000000000 6.000000000 ## ypred[47,1] 2.000000e+00 3.0000000000 6.000000000 ## ypred[48,1] 1.000000e+00 2.0000000000 4.000000000 ## ypred[49,1] 1.000000e+00 2.0000000000 4.000000000 ## ypred[50,1] 1.000000e+00 2.0000000000 3.000000000 ## ypred[51,1] 1.000000e+00 1.0000000000 3.000000000 ## ypred[52,1] 1.000000e+00 1.0000000000 3.000000000 ## ypred[53,1] 1.000000e+00 2.0000000000 3.000000000 ## ypred[54,1] 1.000000e+00 2.0000000000 4.000000000 ## ypred[55,1] 1.000000e+00 2.0000000000 4.000000000 ## ypred[56,1] 2.000000e+00 3.0000000000 6.000000000 ## ypred[57,1] 2.000000e+00 3.0000000000 7.000000000 ## ypred[58,1] 2.000000e+00 3.0000000000 6.000000000 ## ypred[59,1] 2.000000e+00 3.0000000000 6.000000000 ## ypred[60,1] 1.000000e+00 2.0000000000 5.000000000 ## ypred[61,1] 1.000000e+00 2.0000000000 4.000000000 ## ypred[62,1] 1.000000e+00 2.0000000000 4.000000000 ## ypred[63,1] 1.000000e+00 2.0000000000 4.000000000 ## ypred[64,1] 1.000000e+00 2.0000000000 4.000000000 ## ypred[65,1] 1.000000e+00 2.0000000000 4.000000000 ## ypred[66,1] 1.000000e+00 3.0000000000 5.000000000 ## ypred[67,1] 2.000000e+00 3.0000000000 5.000000000 ## ypred[68,1] 3.000000e+00 4.0000000000 7.000000000 ## ypred[69,1] 3.000000e+00 5.0000000000 8.000000000 ## ypred[70,1] 3.000000e+00 5.0000000000 8.000000000 ## ypred[71,1] 2.500000e+00 4.0000000000 6.000000000 ## ypred[72,1] 2.000000e+00 3.0000000000 5.000000000 ## ypred[73,1] 2.000000e+00 3.0000000000 6.000000000 ## ypred[74,1] 2.000000e+00 3.0000000000 5.000000000 ## ypred[75,1] 1.000000e+00 2.0000000000 5.000000000 ## lp__ 6.792385e+01 70.6547000000 75.105087500 ## ## , , chains = chain:2 ## ## stats ## parameter mean sd 2.5% 25% ## alpha_gp[1] 0.6233499580 0.1969450 3.151066e-01 4.809823e-01 ## rho_gp[1] 12.0072589500 8.4461315 2.519005e+00 6.864965e+00 ## b_gp[1,1] 0.0141109737 1.0280355 -2.018255e+00 -5.951910e-01 ## b_gp[2,1] 1.0829920158 0.8052214 -4.433146e-01 5.346483e-01 ## b_gp[3,1] 0.5328896705 0.8637255 -1.315254e+00 -1.690623e-02 ## b_gp[4,1] -1.2010116064 0.8439392 -2.897356e+00 -1.735502e+00 ## b_gp[5,1] -0.7158299553 0.8010451 -2.326940e+00 -1.299900e+00 ## b_gp[6,1] 0.5395176545 0.8178762 -1.087335e+00 -1.984453e-03 ## b_gp[7,1] 0.1922428550 0.8629839 -1.431655e+00 -4.102580e-01 ## b_gp[8,1] 0.0849637441 0.8263355 -1.518549e+00 -5.123645e-01 ## b_gp[9,1] 0.2741316038 0.8432412 -1.435865e+00 -2.606075e-01 ## b_gp[10,1] -0.1366109517 0.9279416 -1.918959e+00 -7.995357e-01 ## b_gp[11,1] -0.6840157925 0.9408062 -2.585943e+00 -1.322095e+00 ## b_gp[12,1] 0.0274666037 0.9249452 -1.682358e+00 -5.509380e-01 ## b_gp[13,1] 0.5277974649 0.9170264 -1.459510e+00 -5.144998e-02 ## b_gp[14,1] 0.2481855499 0.9231580 -1.510770e+00 -4.155647e-01 ## b_gp[15,1] -0.3507100660 0.9799662 -2.245264e+00 -9.771697e-01 ## b_gp[16,1] -0.1244654059 0.9299019 -1.951517e+00 -7.706882e-01 ## b_gp[17,1] 0.3440444082 1.0003079 -1.625322e+00 -3.127140e-01 ## b_gp[18,1] 0.0699463668 0.9088222 -1.766082e+00 -5.307673e-01 ## b_gp[19,1] -0.2285198503 0.9153386 -1.919784e+00 -8.832653e-01 ## b_gp[20,1] -0.0865535057 0.9699989 -1.945997e+00 -7.672372e-01 ## lambda[1] 39.5231547200 19.3445759 9.687419e+00 2.477415e+01 ## trend[1,1] 0.6757130928 0.4629204 -1.485306e-01 3.971917e-01 ## trend[2,1] 0.7083113086 0.4550395 -9.886631e-02 4.492782e-01 ## trend[3,1] 0.7373358569 0.4504790 -7.875349e-02 4.767745e-01 ## trend[4,1] 0.7623944609 0.4486464 -8.454613e-02 5.138563e-01 ## trend[5,1] 0.7830468288 0.4486984 -9.128273e-02 5.536615e-01 ## trend[6,1] 0.7987804593 0.4497864 -8.084896e-02 5.794628e-01 ## trend[7,1] 0.8090046168 0.4512611 -7.413889e-02 5.878792e-01 ## trend[8,1] 0.8130648136 0.4527637 -8.309671e-02 5.860247e-01 ## trend[9,1] 0.8102789108 0.4541910 -1.005743e-01 5.841938e-01 ## trend[10,1] 0.7999922709 0.4555741 -1.243357e-01 5.875177e-01 ## trend[11,1] 0.7816493202 0.4569303 -1.577900e-01 5.688255e-01 ## trend[12,1] 0.7548739881 0.4581615 -2.049020e-01 5.527505e-01 ## trend[13,1] 0.7195492411 0.4590466 -2.329981e-01 5.106617e-01 ## trend[14,1] 0.6758883091 0.4593295 -2.691045e-01 4.739733e-01 ## trend[15,1] 0.6244885706 0.4588611 -3.084546e-01 4.222770e-01 ## trend[16,1] 0.5663582123 0.4577280 -3.484209e-01 3.506948e-01 ## trend[17,1] 0.5029098352 0.4563048 -3.940597e-01 2.862208e-01 ## trend[18,1] 0.4359199847 0.4551867 -4.381635e-01 2.121915e-01 ## trend[19,1] 0.3674514842 0.4550103 -4.920658e-01 1.326995e-01 ## trend[20,1] 0.2997436041 0.4562165 -5.398684e-01 6.371217e-02 ## trend[21,1] 0.2350772973 0.4588517 -5.849397e-01 -2.002430e-02 ## trend[22,1] 0.1756233978 0.4624997 -6.343931e-01 -7.646372e-02 ## trend[23,1] 0.1232881133 0.4663852 -7.042899e-01 -1.401408e-01 ## trend[24,1] 0.0795669159 0.4696056 -7.961698e-01 -1.896707e-01 ## trend[25,1] 0.0454198834 0.4714125 -8.321661e-01 -2.125528e-01 ## trend[26,1] 0.0211812602 0.4714357 -8.466131e-01 -2.298380e-01 ## trend[27,1] 0.0065116152 0.4698046 -8.387186e-01 -2.361510e-01 ## trend[28,1] 0.0003986114 0.4671252 -8.506032e-01 -2.297492e-01 ## trend[29,1] 0.0012087061 0.4643248 -8.853757e-01 -2.375600e-01 ## trend[30,1] 0.0067876768 0.4623881 -9.086242e-01 -2.143227e-01 ## trend[31,1] 0.0146032387 0.4620596 -9.091333e-01 -2.054073e-01 ## trend[32,1] 0.0219199871 0.4636040 -9.315119e-01 -1.934422e-01 ## trend[33,1] 0.0259935241 0.4667189 -9.567011e-01 -2.031268e-01 ## trend[34,1] 0.0242688363 0.4706249 -9.897276e-01 -2.234140e-01 ## trend[35,1] 0.0145681208 0.4742909 -1.021409e+00 -2.200042e-01 ## trend[36,1] -0.0047481205 0.4767124 -1.043683e+00 -2.388145e-01 ## trend[37,1] -0.0346572692 0.4771531 -1.072583e+00 -2.664450e-01 ## trend[38,1] -0.0754000086 0.4753158 -1.107979e+00 -2.962347e-01 ## trend[39,1] -0.1264590465 0.4714206 -1.133731e+00 -3.511337e-01 ## trend[40,1] -0.1865933994 0.4661933 -1.163094e+00 -4.126163e-01 ## trend[41,1] -0.2539249243 0.4607579 -1.190799e+00 -4.765298e-01 ## trend[42,1] -0.3260701253 0.4564272 -1.227312e+00 -5.576375e-01 ## trend[43,1] -0.4003057753 0.4544111 -1.272431e+00 -6.445890e-01 ## trend[44,1] -0.4737560764 0.4554914 -1.366792e+00 -7.242820e-01 ## trend[45,1] -0.5435853946 0.4597761 -1.431630e+00 -7.919597e-01 ## trend[46,1] -0.6071829602 0.4666292 -1.488764e+00 -8.640212e-01 ## trend[47,1] -0.6623234570 0.4748203 -1.589458e+00 -9.220335e-01 ## trend[48,1] -0.7072961570 0.4828286 -1.671874e+00 -9.891910e-01 ## trend[49,1] -0.7409879278 0.4891943 -1.691692e+00 -1.037233e+00 ## trend[50,1] -0.7629209740 0.4928200 -1.693161e+00 -1.062447e+00 ## trend[51,1] -0.7732423428 0.4931743 -1.712381e+00 -1.062582e+00 ## trend[52,1] -0.7726673654 0.4903752 -1.704852e+00 -1.054053e+00 ## trend[53,1] -0.7623853059 0.4851476 -1.675889e+00 -1.044950e+00 ## trend[54,1] -0.7439375708 0.4786659 -1.679524e+00 -1.012992e+00 ## trend[55,1] -0.7190777882 0.4722864 -1.694924e+00 -9.903693e-01 ## trend[56,1] -0.6896262893 0.4672237 -1.635937e+00 -9.490812e-01 ## trend[57,1] -0.6573338198 0.4642562 -1.565669e+00 -9.023412e-01 ## trend[58,1] -0.6237624735 0.4635607 -1.577423e+00 -8.668677e-01 ## trend[59,1] -0.5901923116 0.4647388 -1.583157e+00 -8.433953e-01 ## trend[60,1] -0.5575624626 0.4670184 -1.573111e+00 -8.154685e-01 ## trend[61,1] -0.5264449439 0.4695242 -1.533430e+00 -7.877212e-01 ## trend[62,1] -0.4970554790 0.4715159 -1.512860e+00 -7.706172e-01 ## trend[63,1] -0.4692934306 0.4725200 -1.482261e+00 -7.529195e-01 ## trend[64,1] -0.4428085753 0.4723528 -1.436393e+00 -7.197185e-01 ## trend[65,1] -0.4170829702 0.4710620 -1.407581e+00 -6.835970e-01 ## trend[66,1] -0.3915228426 0.4688428 -1.364900e+00 -6.442542e-01 ## trend[67,1] -0.3655483916 0.4659697 -1.300615e+00 -6.248590e-01 ## trend[68,1] -0.3386754238 0.4627750 -1.245499e+00 -5.918562e-01 ## trend[69,1] -0.3105798063 0.4596622 -1.234330e+00 -5.537173e-01 ## trend[70,1] -0.2811410223 0.4571330 -1.212489e+00 -5.266863e-01 ## trend[71,1] -0.2504612154 0.4557801 -1.177367e+00 -4.967185e-01 ## trend[72,1] -0.2188607588 0.4562226 -1.117777e+00 -4.774897e-01 ## trend[73,1] -0.1868498819 0.4589862 -1.068354e+00 -4.576460e-01 ## trend[74,1] -0.1550826405 0.4643704 -1.047970e+00 -4.243350e-01 ## trend[75,1] -0.1242972250 0.4723651 -1.063384e+00 -4.026565e-01 ## diag_SPD[1,1] 3.2366709260 1.6820764 1.266545e+00 2.047800e+00 ## diag_SPD[2,1] 3.0199574260 1.3581035 1.261107e+00 2.016535e+00 ## diag_SPD[3,1] 2.7387029600 1.0757138 1.255541e+00 1.959260e+00 ## diag_SPD[4,1] 2.4481773300 0.9100254 1.050982e+00 1.829150e+00 ## diag_SPD[5,1] 2.1761652084 0.8342578 7.570662e-01 1.574665e+00 ## diag_SPD[6,1] 1.9316893891 0.7986317 3.192801e-01 1.424743e+00 ## diag_SPD[7,1] 1.7149044952 0.7735611 1.047138e-01 1.278037e+00 ## diag_SPD[8,1] 1.5229777375 0.7494607 2.896879e-02 1.124170e+00 ## diag_SPD[9,1] 1.3527753007 0.7248620 6.364922e-03 9.232915e-01 ## diag_SPD[10,1] 1.2016737595 0.7000392 1.159056e-03 7.375150e-01 ## diag_SPD[11,1] 1.0675783575 0.6752440 1.868947e-04 5.704145e-01 ## diag_SPD[12,1] 0.9487479614 0.6505636 2.608493e-05 4.219152e-01 ## diag_SPD[13,1] 0.8436478224 0.6260552 3.080102e-06 2.885185e-01 ## diag_SPD[14,1] 0.7508718819 0.6018176 3.069995e-07 1.876630e-01 ## diag_SPD[15,1] 0.6691110677 0.5779854 2.408910e-08 1.184030e-01 ## diag_SPD[16,1] 0.5971489706 0.5546953 1.586281e-09 7.203365e-02 ## diag_SPD[17,1] 0.5338643444 0.5320574 8.766725e-11 4.297475e-02 ## diag_SPD[18,1] 0.4782338627 0.5101421 4.066416e-12 2.469658e-02 ## diag_SPD[19,1] 0.4293329446 0.4889835 1.583169e-13 1.395933e-02 ## diag_SPD[20,1] 0.3863314788 0.4685860 5.173776e-15 7.620740e-03 ## SPD_beta[1,1] 0.1045808990 4.2817412 -8.699377e+00 -1.694280e+00 ## SPD_beta[2,1] 2.8430418000 2.1254691 -1.319720e+00 1.543608e+00 ## SPD_beta[3,1] 1.4187030246 2.4914245 -3.623223e+00 -3.189770e-02 ## SPD_beta[4,1] -2.7272517818 1.9800664 -7.113546e+00 -3.885657e+00 ## SPD_beta[5,1] -1.4788870100 1.7203706 -5.322919e+00 -2.573622e+00 ## SPD_beta[6,1] 1.0503445605 1.7685815 -2.128647e+00 2.375601e-03 ## SPD_beta[7,1] 0.3180242512 1.5461671 -2.696174e+00 -6.295790e-01 ## SPD_beta[8,1] 0.1083401065 1.2257076 -2.233956e+00 -6.104297e-01 ## SPD_beta[9,1] 0.4005286121 1.1744906 -1.859880e+00 -2.236185e-01 ## SPD_beta[10,1] -0.2566655240 1.1016936 -2.601640e+00 -9.034488e-01 ## SPD_beta[11,1] -0.7423785367 1.1109529 -3.200625e+00 -1.468243e+00 ## SPD_beta[12,1] -0.0014768048 0.9250191 -2.176973e+00 -4.037243e-01 ## SPD_beta[13,1] 0.5508721689 0.8712450 -7.866410e-01 -1.230252e-06 ## SPD_beta[14,1] 0.2456708802 0.8595120 -1.295221e+00 -1.391308e-01 ## SPD_beta[15,1] -0.2446987227 0.8060298 -1.926307e+00 -5.781975e-01 ## SPD_beta[16,1] -0.1127208017 0.6752985 -1.736458e+00 -3.467027e-01 ## SPD_beta[17,1] 0.2863432335 0.7572487 -8.541044e-01 -1.288387e-02 ## SPD_beta[18,1] 0.0263033010 0.5215951 -1.087509e+00 -8.194325e-02 ## SPD_beta[19,1] -0.1610378483 0.5053986 -1.484157e+00 -2.997608e-01 ## SPD_beta[20,1] -0.0441349805 0.4933585 -1.246651e+00 -1.361243e-01 ## b[1] 0.9776838490 0.4332410 1.509687e-01 7.558113e-01 ## b[2] -0.3615178142 0.1500611 -6.747663e-01 -4.680968e-01 ## b[3] -0.3831897637 0.1760563 -7.073650e-01 -5.048902e-01 ## b[4] -0.1559404000 0.1652868 -5.011194e-01 -2.697892e-01 ## b[5] 0.1465932832 0.1559624 -1.550915e-01 4.138443e-02 ## b[6] 0.5696357480 0.1418283 3.131881e-01 4.672287e-01 ## b[7] 0.3910118061 0.1562433 1.045271e-01 2.863800e-01 ## mus[1,1] 1.6089763940 0.2628555 1.070827e+00 1.444390e+00 ## mus[2,1] 1.4051358060 0.2303241 9.382595e-01 1.269358e+00 ## mus[3,1] 1.3040358300 0.2254216 8.384281e-01 1.169708e+00 ## mus[4,1] 1.3360995460 0.2319538 8.682490e-01 1.183187e+00 ## mus[5,1] 1.4789767240 0.2093349 1.054445e+00 1.351115e+00 ## mus[6,1] 1.6567800400 0.1921560 1.239926e+00 1.542852e+00 ## mus[7,1] 1.8513626600 0.1817486 1.485486e+00 1.725082e+00 ## mus[8,1] 2.1508104800 0.1673810 1.815327e+00 2.048590e+00 ## mus[9,1] 2.3601162200 0.1681139 2.033485e+00 2.246638e+00 ## mus[10,1] 2.2580658600 0.1760093 1.913541e+00 2.146392e+00 ## mus[11,1] 1.9908675600 0.1723860 1.654912e+00 1.867455e+00 ## mus[12,1] 1.6881371000 0.1674812 1.372207e+00 1.585188e+00 ## mus[13,1] 1.6528124800 0.1685259 1.336279e+00 1.549455e+00 ## mus[14,1] 1.3727126440 0.1950547 9.626609e-01 1.243340e+00 ## mus[15,1] 1.1911886900 0.2196253 7.672948e-01 1.043303e+00 ## mus[16,1] 1.1400633800 0.2333223 7.116678e-01 9.887765e-01 ## mus[17,1] 1.1988394660 0.2238200 7.437002e-01 1.059393e+00 ## mus[18,1] 1.2939194080 0.2213142 8.419945e-01 1.160883e+00 ## mus[19,1] 1.4098095320 0.2154724 9.601163e-01 1.274112e+00 ## mus[20,1] 1.6374892380 0.2010079 1.214575e+00 1.502088e+00 ## mus[21,1] 1.7849148600 0.2040593 1.373431e+00 1.640790e+00 ## mus[22,1] 1.6336972000 0.2207815 1.165760e+00 1.492540e+00 ## mus[23,1] 1.3325064220 0.2271469 8.823853e-01 1.179840e+00 ## mus[24,1] 1.0128300400 0.2331666 5.341034e-01 8.669960e-01 ## mus[25,1] 0.9786830506 0.2362314 4.842458e-01 8.332178e-01 ## mus[26,1] 0.7180055916 0.2576769 1.107891e-01 5.672155e-01 ## mus[27,1] 0.5732117747 0.2661221 -2.549527e-04 4.096877e-01 ## mus[28,1] 0.5741036858 0.2624073 6.778035e-02 3.970297e-01 ## mus[29,1] 0.6971386208 0.2387782 1.743854e-01 5.537608e-01 ## mus[30,1] 0.8647869644 0.2206929 4.149347e-01 7.314067e-01 ## mus[31,1] 1.0569612240 0.2070541 6.285449e-01 9.248272e-01 ## mus[32,1] 1.3596656300 0.1915324 9.944129e-01 1.239427e+00 ## mus[33,1] 1.5758310940 0.1990263 1.196894e+00 1.431672e+00 ## mus[34,1] 1.4823426560 0.2249628 1.062197e+00 1.337207e+00 ## mus[35,1] 1.2237863100 0.2324777 7.843894e-01 1.060547e+00 ## mus[36,1] 0.9285150660 0.2310775 5.045983e-01 7.655417e-01 ## mus[37,1] 0.8986059180 0.2371952 4.594818e-01 7.284702e-01 ## mus[38,1] 0.6214242595 0.2558216 1.184572e-01 4.513073e-01 ## mus[39,1] 0.4402411182 0.2697158 -9.005071e-02 2.624850e-01 ## mus[40,1] 0.3871116954 0.2726654 -1.963161e-01 1.970850e-01 ## mus[41,1] 0.4420048301 0.2475564 -2.494371e-02 2.830918e-01 ## mus[42,1] 0.5319292637 0.2335572 5.727740e-02 3.695833e-01 ## mus[43,1] 0.6420522246 0.2357230 1.935359e-01 4.828443e-01 ## mus[44,1] 0.8639893668 0.2333490 3.782997e-01 7.190192e-01 ## mus[45,1] 1.0062522560 0.2428634 5.047268e-01 8.478855e-01 ## mus[46,1] 0.8508909260 0.2593719 3.053446e-01 6.790912e-01 ## mus[47,1] 0.5468947002 0.2739351 -3.386320e-02 3.804903e-01 ## mus[48,1] 0.2259669595 0.2874446 -3.643873e-01 5.587088e-02 ## mus[49,1] 0.1922752302 0.2973652 -4.209943e-01 1.579140e-02 ## mus[50,1] -0.0660968263 0.3099469 -7.256560e-01 -2.740843e-01 ## mus[51,1] -0.2065422183 0.3271980 -8.810435e-01 -4.296760e-01 ## mus[52,1] -0.1989621851 0.3447650 -9.379764e-01 -4.466650e-01 ## mus[53,1] -0.0664554175 0.3253713 -7.417035e-01 -2.969993e-01 ## mus[54,1] 0.1140617192 0.2988879 -4.937733e-01 -8.045912e-02 ## mus[55,1] 0.3232802549 0.2773109 -2.422552e-01 1.338743e-01 ## mus[56,1] 0.6481194137 0.2574348 1.160112e-01 4.796507e-01 ## mus[57,1] 0.8925038320 0.2523172 3.477859e-01 7.417288e-01 ## mus[58,1] 0.8343112420 0.2558893 2.873121e-01 6.655433e-01 ## mus[59,1] 0.6190259160 0.2536558 1.269790e-01 4.482095e-01 ## mus[60,1] 0.3757007634 0.2532114 -1.123731e-01 2.091223e-01 ## mus[61,1] 0.4068181980 0.2552577 -9.347024e-02 2.303022e-01 ## mus[62,1] 0.1997688152 0.2771621 -3.924211e-01 3.321702e-02 ## mus[63,1] 0.0974066591 0.2891421 -4.948088e-01 -8.022855e-02 ## mus[64,1] 0.1308964409 0.2852334 -4.830208e-01 -4.024458e-02 ## mus[65,1] 0.2788468308 0.2665662 -2.921954e-01 1.044068e-01 ## mus[66,1] 0.4664765659 0.2556770 -6.330473e-02 3.109700e-01 ## mus[67,1] 0.6768096502 0.2404863 1.899065e-01 5.133485e-01 ## mus[68,1] 0.9990702020 0.2206026 5.574431e-01 8.572068e-01 ## mus[69,1] 1.2392579240 0.2163549 8.368891e-01 1.091530e+00 ## mus[70,1] 1.1769326660 0.2243226 7.276244e-01 1.037883e+00 ## mus[71,1] 0.9587569400 0.2250119 5.156652e-01 8.117998e-01 ## mus[72,1] 0.7144024021 0.2281142 2.418463e-01 5.720640e-01 ## mus[73,1] 0.7464132937 0.2455775 2.349489e-01 5.921692e-01 ## mus[74,1] 0.5417415834 0.2782289 1.186370e-02 3.476285e-01 ## mus[75,1] 0.4424029133 0.3177067 -1.299212e-01 2.346440e-01 ## rho[1] 3.5429865200 0.5492388 2.270822e+00 3.209792e+00 ## ypred[1,1] 5.2440000000 2.6454604 1.000000e+00 3.000000e+00 ## ypred[2,1] 4.1800000000 2.2551655 0.000000e+00 3.000000e+00 ## ypred[3,1] 3.7600000000 2.1798862 0.000000e+00 2.000000e+00 ## ypred[4,1] 3.8860000000 2.0817472 1.000000e+00 2.000000e+00 ## ypred[5,1] 4.3940000000 2.2344461 1.000000e+00 3.000000e+00 ## ypred[6,1] 5.1240000000 2.5654995 1.000000e+00 3.000000e+00 ## ypred[7,1] 6.3940000000 2.8381109 2.000000e+00 4.000000e+00 ## ypred[8,1] 8.7000000000 3.2103914 3.000000e+00 6.750000e+00 ## ypred[9,1] 10.6460000000 3.6451692 5.000000e+00 8.000000e+00 ## ypred[10,1] 9.7180000000 3.4880954 4.000000e+00 7.000000e+00 ## ypred[11,1] 7.2960000000 2.8839241 2.000000e+00 5.000000e+00 ## ypred[12,1] 5.2660000000 2.4542393 1.000000e+00 3.750000e+00 ## ypred[13,1] 5.2900000000 2.3734292 1.000000e+00 4.000000e+00 ## ypred[14,1] 4.0940000000 2.2015580 0.000000e+00 2.000000e+00 ## ypred[15,1] 3.5160000000 1.9944171 0.000000e+00 2.000000e+00 ## ypred[16,1] 3.2300000000 1.8417068 0.000000e+00 2.000000e+00 ## ypred[17,1] 3.3940000000 1.9785331 0.000000e+00 2.000000e+00 ## ypred[18,1] 3.7040000000 2.1083820 0.000000e+00 2.000000e+00 ## ypred[19,1] 4.2820000000 2.2699739 4.750000e-01 3.000000e+00 ## ypred[20,1] 5.2220000000 2.4610627 1.000000e+00 4.000000e+00 ## ypred[21,1] 6.2380000000 2.7210594 2.000000e+00 4.000000e+00 ## ypred[22,1] 5.4160000000 2.5714137 1.000000e+00 4.000000e+00 ## ypred[23,1] 3.7600000000 2.0907277 0.000000e+00 2.000000e+00 ## ypred[24,1] 2.7240000000 1.7635317 0.000000e+00 1.000000e+00 ## ypred[25,1] 2.8020000000 1.7756977 0.000000e+00 1.000000e+00 ## ypred[26,1] 2.0840000000 1.5024842 0.000000e+00 1.000000e+00 ## ypred[27,1] 1.8780000000 1.4925050 0.000000e+00 1.000000e+00 ## ypred[28,1] 1.7760000000 1.4676962 0.000000e+00 1.000000e+00 ## ypred[29,1] 2.0100000000 1.4415464 0.000000e+00 1.000000e+00 ## ypred[30,1] 2.4880000000 1.7595591 0.000000e+00 1.000000e+00 ## ypred[31,1] 2.9720000000 1.9053811 0.000000e+00 2.000000e+00 ## ypred[32,1] 3.9280000000 2.0344764 1.000000e+00 2.000000e+00 ## ypred[33,1] 5.0400000000 2.4784441 1.000000e+00 3.000000e+00 ## ypred[34,1] 4.5300000000 2.5103194 1.000000e+00 3.000000e+00 ## ypred[35,1] 3.4580000000 2.0080589 0.000000e+00 2.000000e+00 ## ypred[36,1] 2.6380000000 1.8947655 0.000000e+00 1.000000e+00 ## ypred[37,1] 2.5860000000 1.7733848 0.000000e+00 1.000000e+00 ## ypred[38,1] 1.8720000000 1.4267752 0.000000e+00 1.000000e+00 ## ypred[39,1] 1.7180000000 1.3513431 0.000000e+00 1.000000e+00 ## ypred[40,1] 1.5440000000 1.3219528 0.000000e+00 0.000000e+00 ## ypred[41,1] 1.5840000000 1.3967268 0.000000e+00 1.000000e+00 ## ypred[42,1] 1.7100000000 1.3555719 0.000000e+00 1.000000e+00 ## ypred[43,1] 1.9600000000 1.4305569 0.000000e+00 1.000000e+00 ## ypred[44,1] 2.5420000000 1.6473200 0.000000e+00 1.000000e+00 ## ypred[45,1] 2.8260000000 1.8456807 0.000000e+00 1.000000e+00 ## ypred[46,1] 2.4720000000 1.7271892 0.000000e+00 1.000000e+00 ## ypred[47,1] 1.7860000000 1.3295636 0.000000e+00 1.000000e+00 ## ypred[48,1] 1.3000000000 1.2037017 0.000000e+00 0.000000e+00 ## ypred[49,1] 1.2360000000 1.1606024 0.000000e+00 0.000000e+00 ## ypred[50,1] 0.8780000000 0.9762285 0.000000e+00 0.000000e+00 ## ypred[51,1] 0.8220000000 0.9634170 0.000000e+00 0.000000e+00 ## ypred[52,1] 0.8340000000 0.9252872 0.000000e+00 0.000000e+00 ## ypred[53,1] 0.9640000000 1.0201890 0.000000e+00 0.000000e+00 ## ypred[54,1] 1.2200000000 1.1706155 0.000000e+00 0.000000e+00 ## ypred[55,1] 1.4380000000 1.2511141 0.000000e+00 1.000000e+00 ## ypred[56,1] 1.8240000000 1.4244586 0.000000e+00 1.000000e+00 ## ypred[57,1] 2.5600000000 1.6935573 0.000000e+00 1.000000e+00 ## ypred[58,1] 2.2480000000 1.5528421 0.000000e+00 1.000000e+00 ## ypred[59,1] 1.8400000000 1.4541765 0.000000e+00 1.000000e+00 ## ypred[60,1] 1.5040000000 1.3644440 0.000000e+00 0.000000e+00 ## ypred[61,1] 1.5900000000 1.4006512 0.000000e+00 1.000000e+00 ## ypred[62,1] 1.2040000000 1.1597733 0.000000e+00 0.000000e+00 ## ypred[63,1] 1.1980000000 1.1230844 0.000000e+00 0.000000e+00 ## ypred[64,1] 1.1780000000 1.1510716 0.000000e+00 0.000000e+00 ## ypred[65,1] 1.4060000000 1.2602939 0.000000e+00 0.000000e+00 ## ypred[66,1] 1.5820000000 1.2878638 0.000000e+00 1.000000e+00 ## ypred[67,1] 2.0440000000 1.5161337 0.000000e+00 1.000000e+00 ## ypred[68,1] 2.7220000000 1.7997762 0.000000e+00 1.000000e+00 ## ypred[69,1] 3.5500000000 2.1430551 0.000000e+00 2.000000e+00 ## ypred[70,1] 3.3420000000 1.8910813 0.000000e+00 2.000000e+00 ## ypred[71,1] 2.5920000000 1.7214712 0.000000e+00 1.000000e+00 ## ypred[72,1] 2.1340000000 1.5559196 0.000000e+00 1.000000e+00 ## ypred[73,1] 2.2160000000 1.5132494 0.000000e+00 1.000000e+00 ## ypred[74,1] 1.8720000000 1.4980334 0.000000e+00 1.000000e+00 ## ypred[75,1] 1.6100000000 1.4134694 0.000000e+00 1.000000e+00 ## lp__ 66.7411050000 4.8325098 5.678678e+01 6.335408e+01 ## stats ## parameter 50% 75% 97.5% ## alpha_gp[1] 5.971230e-01 7.402770e-01 1.07388950 ## rho_gp[1] 9.551150e+00 1.445768e+01 34.91129250 ## b_gp[1,1] 2.395375e-02 7.236940e-01 2.02506150 ## b_gp[2,1] 1.057415e+00 1.609040e+00 2.68884500 ## b_gp[3,1] 5.366095e-01 1.149695e+00 2.05869050 ## b_gp[4,1] -1.158750e+00 -7.124235e-01 0.48427397 ## b_gp[5,1] -6.891265e-01 -1.772660e-01 0.84154250 ## b_gp[6,1] 5.395500e-01 1.103990e+00 2.11123300 ## b_gp[7,1] 1.817275e-01 8.108928e-01 1.96030775 ## b_gp[8,1] 5.121010e-02 7.080262e-01 1.58130025 ## b_gp[9,1] 3.212130e-01 8.251495e-01 1.91343900 ## b_gp[10,1] -1.667975e-01 4.543445e-01 1.82697250 ## b_gp[11,1] -6.735805e-01 -5.172177e-02 1.02736475 ## b_gp[12,1] 1.991260e-02 5.867098e-01 1.95489500 ## b_gp[13,1] 5.444375e-01 1.118520e+00 2.18546425 ## b_gp[14,1] 2.327355e-01 9.194450e-01 1.97041650 ## b_gp[15,1] -3.555450e-01 2.577368e-01 1.72783975 ## b_gp[16,1] -1.397620e-01 4.745922e-01 1.75310300 ## b_gp[17,1] 3.203380e-01 9.684052e-01 2.39142850 ## b_gp[18,1] 1.186135e-01 7.214868e-01 1.70606600 ## b_gp[19,1] -2.795355e-01 3.752955e-01 1.68072550 ## b_gp[20,1] -6.811885e-02 4.838153e-01 1.91305650 ## lambda[1] 3.749905e+01 5.096180e+01 83.78450000 ## trend[1,1] 6.660155e-01 9.269045e-01 1.60750200 ## trend[2,1] 7.028725e-01 9.449675e-01 1.69918950 ## trend[3,1] 7.370900e-01 9.625368e-01 1.77019825 ## trend[4,1] 7.633620e-01 1.004720e+00 1.81129450 ## trend[5,1] 7.835125e-01 1.016898e+00 1.80439325 ## trend[6,1] 7.957020e-01 1.014235e+00 1.79062200 ## trend[7,1] 8.124805e-01 1.016020e+00 1.77112275 ## trend[8,1] 8.230920e-01 1.019465e+00 1.75456275 ## trend[9,1] 8.218355e-01 1.032357e+00 1.72417950 ## trend[10,1] 8.159330e-01 1.037395e+00 1.70776700 ## trend[11,1] 7.896145e-01 1.020875e+00 1.65662625 ## trend[12,1] 7.651935e-01 9.983358e-01 1.64743475 ## trend[13,1] 7.252330e-01 9.623498e-01 1.60430700 ## trend[14,1] 6.760075e-01 9.185950e-01 1.53877225 ## trend[15,1] 6.283235e-01 8.680645e-01 1.49268150 ## trend[16,1] 5.652045e-01 8.071555e-01 1.43442350 ## trend[17,1] 5.012320e-01 7.460335e-01 1.36624650 ## trend[18,1] 4.357805e-01 6.744000e-01 1.29089375 ## trend[19,1] 3.688030e-01 5.917325e-01 1.22002950 ## trend[20,1] 3.087215e-01 5.273598e-01 1.17908125 ## trend[21,1] 2.391140e-01 4.628523e-01 1.14061475 ## trend[22,1] 1.779940e-01 3.973782e-01 1.09994875 ## trend[23,1] 1.279630e-01 3.499080e-01 1.06225825 ## trend[24,1] 8.702640e-02 3.096000e-01 1.03042150 ## trend[25,1] 4.520050e-02 2.792697e-01 1.00386050 ## trend[26,1] 2.240260e-02 2.598380e-01 0.98504275 ## trend[27,1] 1.267200e-02 2.494730e-01 0.97720267 ## trend[28,1] 3.901270e-03 2.377907e-01 0.96990190 ## trend[29,1] -2.633110e-03 2.332540e-01 0.95489640 ## trend[30,1] 1.169205e-02 2.366117e-01 0.93512072 ## trend[31,1] 2.045930e-02 2.432725e-01 0.91415237 ## trend[32,1] 2.965850e-02 2.554838e-01 0.89815070 ## trend[33,1] 3.768545e-02 2.680575e-01 0.90160280 ## trend[34,1] 4.125075e-02 2.753093e-01 0.92409253 ## trend[35,1] 4.434510e-02 2.814885e-01 0.90782325 ## trend[36,1] 1.889540e-02 2.720850e-01 0.88867173 ## trend[37,1] -1.089385e-02 2.449123e-01 0.85502172 ## trend[38,1] -6.314130e-02 2.037667e-01 0.79094427 ## trend[39,1] -1.199325e-01 1.419233e-01 0.73002575 ## trend[40,1] -1.825865e-01 7.394867e-02 0.66026350 ## trend[41,1] -2.537495e-01 1.130758e-02 0.61050427 ## trend[42,1] -3.237090e-01 -7.010358e-02 0.54974665 ## trend[43,1] -4.020785e-01 -1.430730e-01 0.49738635 ## trend[44,1] -4.746530e-01 -2.326012e-01 0.43374297 ## trend[45,1] -5.518480e-01 -3.006652e-01 0.36824677 ## trend[46,1] -6.056820e-01 -3.577920e-01 0.31901180 ## trend[47,1] -6.699365e-01 -3.996453e-01 0.28202315 ## trend[48,1] -7.271610e-01 -4.415495e-01 0.27259990 ## trend[49,1] -7.676335e-01 -4.653827e-01 0.27770707 ## trend[50,1] -7.746255e-01 -4.759667e-01 0.25692122 ## trend[51,1] -7.844460e-01 -4.863275e-01 0.23021817 ## trend[52,1] -7.886515e-01 -4.890780e-01 0.20210400 ## trend[53,1] -7.679130e-01 -4.815960e-01 0.18238677 ## trend[54,1] -7.478360e-01 -4.523497e-01 0.17125772 ## trend[55,1] -7.230835e-01 -4.235995e-01 0.17162290 ## trend[56,1] -6.918125e-01 -3.975158e-01 0.17833410 ## trend[57,1] -6.617720e-01 -3.703093e-01 0.17579457 ## trend[58,1] -6.232485e-01 -3.364515e-01 0.22546042 ## trend[59,1] -5.707030e-01 -2.986635e-01 0.24931907 ## trend[60,1] -5.371300e-01 -2.688495e-01 0.25369820 ## trend[61,1] -5.012540e-01 -2.272155e-01 0.26673780 ## trend[62,1] -4.691735e-01 -1.883365e-01 0.30198817 ## trend[63,1] -4.423215e-01 -1.726972e-01 0.34783552 ## trend[64,1] -4.093470e-01 -1.445333e-01 0.38100092 ## trend[65,1] -4.056705e-01 -1.232318e-01 0.44880802 ## trend[66,1] -3.821715e-01 -1.016043e-01 0.51423480 ## trend[67,1] -3.637335e-01 -8.313970e-02 0.60135087 ## trend[68,1] -3.445790e-01 -7.611638e-02 0.68466387 ## trend[69,1] -3.088155e-01 -4.231395e-02 0.73672047 ## trend[70,1] -2.775050e-01 -2.290852e-02 0.74656745 ## trend[71,1] -2.358360e-01 -2.551693e-03 0.76745762 ## trend[72,1] -2.051310e-01 2.463495e-02 0.80111390 ## trend[73,1] -1.774160e-01 6.398975e-02 0.78531490 ## trend[74,1] -1.570310e-01 1.212517e-01 0.84309267 ## trend[75,1] -1.219475e-01 1.608837e-01 0.86418620 ## diag_SPD[1,1] 2.759770e+00 4.011913e+00 8.05257250 ## diag_SPD[2,1] 2.702140e+00 3.806068e+00 6.68795525 ## diag_SPD[3,1] 2.543830e+00 3.377833e+00 5.28875100 ## diag_SPD[4,1] 2.287180e+00 2.921723e+00 4.41067150 ## diag_SPD[5,1] 2.056635e+00 2.685070e+00 3.96372800 ## diag_SPD[6,1] 1.911395e+00 2.427715e+00 3.51794225 ## diag_SPD[7,1] 1.750920e+00 2.201353e+00 3.25101100 ## diag_SPD[8,1] 1.577475e+00 2.000522e+00 3.02025575 ## diag_SPD[9,1] 1.406245e+00 1.838910e+00 2.69090325 ## diag_SPD[10,1] 1.263025e+00 1.704290e+00 2.51017400 ## diag_SPD[11,1] 1.121425e+00 1.548123e+00 2.33551825 ## diag_SPD[12,1] 9.831370e-01 1.393832e+00 2.18456325 ## diag_SPD[13,1] 8.775535e-01 1.274358e+00 2.05716200 ## diag_SPD[14,1] 7.468065e-01 1.162312e+00 1.97027575 ## diag_SPD[15,1] 6.341210e-01 1.048895e+00 1.89151875 ## diag_SPD[16,1] 5.210030e-01 9.425040e-01 1.82319400 ## diag_SPD[17,1] 4.269445e-01 8.467478e-01 1.71100025 ## diag_SPD[18,1] 3.468075e-01 7.696775e-01 1.63061525 ## diag_SPD[19,1] 2.746280e-01 6.855947e-01 1.56841750 ## diag_SPD[20,1] 2.114190e-01 5.876752e-01 1.53329075 ## SPD_beta[1,1] 6.881305e-02 1.794555e+00 8.85716525 ## SPD_beta[2,1] 2.745255e+00 4.056965e+00 7.36002750 ## SPD_beta[3,1] 1.439800e+00 2.858532e+00 6.83111425 ## SPD_beta[4,1] -2.685535e+00 -1.379233e+00 0.95108132 ## SPD_beta[5,1] -1.499550e+00 -2.768383e-01 1.62093875 ## SPD_beta[6,1] 8.543515e-01 1.924233e+00 4.80325850 ## SPD_beta[7,1] 2.139400e-01 1.304490e+00 3.61366575 ## SPD_beta[8,1] 2.561655e-02 9.276463e-01 2.42910775 ## SPD_beta[9,1] 2.527325e-01 1.066880e+00 2.94880925 ## SPD_beta[10,1] -6.713075e-02 2.564382e-01 2.00518925 ## SPD_beta[11,1] -5.339445e-01 -8.426337e-05 1.16952625 ## SPD_beta[12,1] 4.903485e-05 4.150923e-01 1.87520100 ## SPD_beta[13,1] 3.030130e-01 1.044468e+00 2.62296050 ## SPD_beta[14,1] 3.690545e-02 5.669185e-01 2.34768400 ## SPD_beta[15,1] -4.385895e-02 2.838388e-02 1.31547475 ## SPD_beta[16,1] -2.294805e-03 6.763273e-02 1.29896800 ## SPD_beta[17,1] 1.678500e-02 4.997745e-01 2.39964600 ## SPD_beta[18,1] 2.233855e-07 1.814515e-01 1.08687775 ## SPD_beta[19,1] -3.722295e-03 1.495780e-02 0.71397880 ## SPD_beta[20,1] -2.819260e-12 4.805572e-02 0.93627597 ## b[1] 9.600185e-01 1.180028e+00 1.85881700 ## b[2] -3.534595e-01 -2.619895e-01 -0.08650899 ## b[3] -3.811275e-01 -2.681512e-01 -0.03192457 ## b[4] -1.579875e-01 -3.266238e-02 0.13286965 ## b[5] 1.549530e-01 2.469638e-01 0.45522547 ## b[6] 5.681770e-01 6.624773e-01 0.86001982 ## b[7] 3.872580e-01 4.943455e-01 0.72757815 ## mus[1,1] 1.617130e+00 1.784273e+00 2.11250475 ## mus[2,1] 1.419320e+00 1.552955e+00 1.82860700 ## mus[3,1] 1.304050e+00 1.454382e+00 1.69117900 ## mus[4,1] 1.333110e+00 1.489965e+00 1.77793325 ## mus[5,1] 1.490285e+00 1.612220e+00 1.86170700 ## mus[6,1] 1.654995e+00 1.784730e+00 2.02962700 ## mus[7,1] 1.848005e+00 1.979807e+00 2.21236850 ## mus[8,1] 2.154260e+00 2.261620e+00 2.48420425 ## mus[9,1] 2.360025e+00 2.462498e+00 2.70022325 ## mus[10,1] 2.247360e+00 2.378808e+00 2.60685125 ## mus[11,1] 1.993085e+00 2.120507e+00 2.30398025 ## mus[12,1] 1.679670e+00 1.798738e+00 2.00131550 ## mus[13,1] 1.648140e+00 1.767252e+00 1.97424425 ## mus[14,1] 1.372755e+00 1.503310e+00 1.73798175 ## mus[15,1] 1.180200e+00 1.335865e+00 1.63312550 ## mus[16,1] 1.126945e+00 1.297210e+00 1.60394225 ## mus[17,1] 1.194235e+00 1.354250e+00 1.63811700 ## mus[18,1] 1.299980e+00 1.443868e+00 1.71174125 ## mus[19,1] 1.417875e+00 1.554822e+00 1.80335850 ## mus[20,1] 1.654495e+00 1.777930e+00 2.00015900 ## mus[21,1] 1.798925e+00 1.919482e+00 2.17638325 ## mus[22,1] 1.629775e+00 1.785168e+00 2.03829150 ## mus[23,1] 1.356595e+00 1.492440e+00 1.72756550 ## mus[24,1] 1.039015e+00 1.183465e+00 1.40821600 ## mus[25,1] 1.005695e+00 1.147213e+00 1.39198400 ## mus[26,1] 7.481485e-01 8.901467e-01 1.13766325 ## mus[27,1] 6.051145e-01 7.589792e-01 1.01731175 ## mus[28,1] 5.822775e-01 7.623170e-01 1.01576475 ## mus[29,1] 7.071930e-01 8.479073e-01 1.14057800 ## mus[30,1] 8.653465e-01 1.012983e+00 1.26586450 ## mus[31,1] 1.064075e+00 1.197415e+00 1.44037400 ## mus[32,1] 1.358140e+00 1.480808e+00 1.75685275 ## mus[33,1] 1.575630e+00 1.710950e+00 1.97546700 ## mus[34,1] 1.478230e+00 1.633335e+00 1.92583225 ## mus[35,1] 1.223815e+00 1.384842e+00 1.67633650 ## mus[36,1] 9.222355e-01 1.097128e+00 1.37411175 ## mus[37,1] 8.848185e-01 1.070525e+00 1.37565425 ## mus[38,1] 6.126765e-01 8.007600e-01 1.13990075 ## mus[39,1] 4.450840e-01 6.196613e-01 0.95394472 ## mus[40,1] 3.959415e-01 5.838225e-01 0.91542590 ## mus[41,1] 4.221135e-01 6.217182e-01 0.91362730 ## mus[42,1] 5.239945e-01 6.888007e-01 1.00676350 ## mus[43,1] 6.486445e-01 8.158043e-01 1.09160175 ## mus[44,1] 8.814730e-01 1.025143e+00 1.30800275 ## mus[45,1] 1.026840e+00 1.175833e+00 1.43387250 ## mus[46,1] 8.700695e-01 1.031520e+00 1.28749500 ## mus[47,1] 5.563840e-01 7.322198e-01 1.04652000 ## mus[48,1] 2.384400e-01 4.238397e-01 0.73198703 ## mus[49,1] 2.033375e-01 4.006720e-01 0.72014872 ## mus[50,1] -4.244180e-02 1.425298e-01 0.52420267 ## mus[51,1] -1.752115e-01 2.435837e-02 0.39314247 ## mus[52,1] -1.712395e-01 3.290240e-02 0.43953052 ## mus[53,1] -4.347620e-02 1.688650e-01 0.48841615 ## mus[54,1] 1.206120e-01 3.173728e-01 0.64807917 ## mus[55,1] 3.434425e-01 5.121107e-01 0.80816605 ## mus[56,1] 6.622295e-01 8.164375e-01 1.15030725 ## mus[57,1] 9.069525e-01 1.059783e+00 1.39601825 ## mus[58,1] 8.381730e-01 9.984717e-01 1.31583175 ## mus[59,1] 6.125665e-01 7.892960e-01 1.09045350 ## mus[60,1] 3.822165e-01 5.286628e-01 0.87238288 ## mus[61,1] 4.146640e-01 5.614405e-01 0.90232090 ## mus[62,1] 2.023065e-01 3.770405e-01 0.73699400 ## mus[63,1] 1.172405e-01 2.800810e-01 0.62115020 ## mus[64,1] 1.423395e-01 3.089343e-01 0.65912107 ## mus[65,1] 2.771175e-01 4.688682e-01 0.75262142 ## mus[66,1] 4.640590e-01 6.253963e-01 0.95701880 ## mus[67,1] 6.818140e-01 8.370845e-01 1.17234125 ## mus[68,1] 9.915480e-01 1.150505e+00 1.43498675 ## mus[69,1] 1.231730e+00 1.392130e+00 1.64144400 ## mus[70,1] 1.174115e+00 1.328285e+00 1.61334900 ## mus[71,1] 9.565095e-01 1.103585e+00 1.38863525 ## mus[72,1] 7.104560e-01 8.742212e-01 1.14605200 ## mus[73,1] 7.429210e-01 9.070050e-01 1.21139775 ## mus[74,1] 5.344145e-01 7.424047e-01 1.08609700 ## mus[75,1] 4.292610e-01 6.414882e-01 1.07244375 ## rho[1] 3.624315e+00 3.931072e+00 4.42824450 ## ypred[1,1] 5.000000e+00 7.000000e+00 11.00000000 ## ypred[2,1] 4.000000e+00 6.000000e+00 9.00000000 ## ypred[3,1] 3.000000e+00 5.000000e+00 9.00000000 ## ypred[4,1] 4.000000e+00 5.000000e+00 9.00000000 ## ypred[5,1] 4.000000e+00 6.000000e+00 9.52500000 ## ypred[6,1] 5.000000e+00 7.000000e+00 11.00000000 ## ypred[7,1] 6.000000e+00 8.000000e+00 13.00000000 ## ypred[8,1] 8.000000e+00 1.100000e+01 16.00000000 ## ypred[9,1] 1.000000e+01 1.300000e+01 18.00000000 ## ypred[10,1] 9.000000e+00 1.200000e+01 17.00000000 ## ypred[11,1] 7.000000e+00 9.000000e+00 13.00000000 ## ypred[12,1] 5.000000e+00 7.000000e+00 10.00000000 ## ypred[13,1] 5.000000e+00 7.000000e+00 10.00000000 ## ypred[14,1] 4.000000e+00 6.000000e+00 9.00000000 ## ypred[15,1] 3.000000e+00 5.000000e+00 8.00000000 ## ypred[16,1] 3.000000e+00 4.000000e+00 7.00000000 ## ypred[17,1] 3.000000e+00 5.000000e+00 7.00000000 ## ypred[18,1] 3.000000e+00 5.000000e+00 8.00000000 ## ypred[19,1] 4.000000e+00 6.000000e+00 9.00000000 ## ypred[20,1] 5.000000e+00 7.000000e+00 10.00000000 ## ypred[21,1] 6.000000e+00 8.000000e+00 12.00000000 ## ypred[22,1] 5.000000e+00 7.000000e+00 11.00000000 ## ypred[23,1] 4.000000e+00 5.000000e+00 8.52500000 ## ypred[24,1] 3.000000e+00 4.000000e+00 6.00000000 ## ypred[25,1] 3.000000e+00 4.000000e+00 7.00000000 ## ypred[26,1] 2.000000e+00 3.000000e+00 6.00000000 ## ypred[27,1] 2.000000e+00 3.000000e+00 5.00000000 ## ypred[28,1] 2.000000e+00 3.000000e+00 5.00000000 ## ypred[29,1] 2.000000e+00 3.000000e+00 5.00000000 ## ypred[30,1] 2.000000e+00 4.000000e+00 6.00000000 ## ypred[31,1] 3.000000e+00 4.000000e+00 7.00000000 ## ypred[32,1] 4.000000e+00 5.000000e+00 8.00000000 ## ypred[33,1] 5.000000e+00 6.000000e+00 11.00000000 ## ypred[34,1] 4.000000e+00 6.000000e+00 10.52500000 ## ypred[35,1] 3.000000e+00 5.000000e+00 8.00000000 ## ypred[36,1] 2.000000e+00 4.000000e+00 7.00000000 ## ypred[37,1] 2.000000e+00 4.000000e+00 7.00000000 ## ypred[38,1] 2.000000e+00 3.000000e+00 5.00000000 ## ypred[39,1] 1.000000e+00 3.000000e+00 5.00000000 ## ypred[40,1] 1.000000e+00 2.000000e+00 5.00000000 ## ypred[41,1] 1.000000e+00 2.000000e+00 5.00000000 ## ypred[42,1] 2.000000e+00 3.000000e+00 5.00000000 ## ypred[43,1] 2.000000e+00 3.000000e+00 5.00000000 ## ypred[44,1] 2.000000e+00 3.000000e+00 6.00000000 ## ypred[45,1] 3.000000e+00 4.000000e+00 7.00000000 ## ypred[46,1] 2.000000e+00 3.000000e+00 6.52500000 ## ypred[47,1] 2.000000e+00 3.000000e+00 5.00000000 ## ypred[48,1] 1.000000e+00 2.000000e+00 4.00000000 ## ypred[49,1] 1.000000e+00 2.000000e+00 4.00000000 ## ypred[50,1] 1.000000e+00 1.000000e+00 3.00000000 ## ypred[51,1] 1.000000e+00 1.000000e+00 3.00000000 ## ypred[52,1] 1.000000e+00 1.000000e+00 3.00000000 ## ypred[53,1] 1.000000e+00 2.000000e+00 3.00000000 ## ypred[54,1] 1.000000e+00 2.000000e+00 4.00000000 ## ypred[55,1] 1.000000e+00 2.000000e+00 4.00000000 ## ypred[56,1] 2.000000e+00 3.000000e+00 5.00000000 ## ypred[57,1] 2.000000e+00 4.000000e+00 6.00000000 ## ypred[58,1] 2.000000e+00 3.000000e+00 6.00000000 ## ypred[59,1] 2.000000e+00 3.000000e+00 5.00000000 ## ypred[60,1] 1.000000e+00 2.000000e+00 5.00000000 ## ypred[61,1] 1.000000e+00 2.000000e+00 5.00000000 ## ypred[62,1] 1.000000e+00 2.000000e+00 4.00000000 ## ypred[63,1] 1.000000e+00 2.000000e+00 4.00000000 ## ypred[64,1] 1.000000e+00 2.000000e+00 4.00000000 ## ypred[65,1] 1.000000e+00 2.000000e+00 4.00000000 ## ypred[66,1] 1.000000e+00 2.000000e+00 4.00000000 ## ypred[67,1] 2.000000e+00 3.000000e+00 5.00000000 ## ypred[68,1] 2.000000e+00 4.000000e+00 6.52500000 ## ypred[69,1] 3.000000e+00 5.000000e+00 8.00000000 ## ypred[70,1] 3.000000e+00 5.000000e+00 7.00000000 ## ypred[71,1] 2.000000e+00 3.000000e+00 7.00000000 ## ypred[72,1] 2.000000e+00 3.000000e+00 6.00000000 ## ypred[73,1] 2.000000e+00 3.000000e+00 5.00000000 ## ypred[74,1] 2.000000e+00 3.000000e+00 5.00000000 ## ypred[75,1] 1.000000e+00 2.000000e+00 5.00000000 ## lp__ 6.700965e+01 7.026195e+01 74.83527000 ## ## , , chains = chain:3 ## ## stats ## parameter mean sd 2.5% 25% ## alpha_gp[1] 0.609116538 0.1848074 3.469831e-01 0.468860750 ## rho_gp[1] 12.478711440 8.7275070 2.146605e+00 6.526585000 ## b_gp[1,1] -0.083609565 0.9109411 -1.856612e+00 -0.736606500 ## b_gp[2,1] 1.031689397 0.7307019 -4.792724e-01 0.576688500 ## b_gp[3,1] 0.560948209 0.8555712 -1.129021e+00 -0.012013200 ## b_gp[4,1] -1.259614768 0.7924411 -2.896872e+00 -1.785447500 ## b_gp[5,1] -0.711108655 0.7551405 -2.065881e+00 -1.284960000 ## b_gp[6,1] 0.617150631 0.8500395 -9.699530e-01 0.071584325 ## b_gp[7,1] 0.215133350 0.8485863 -1.421778e+00 -0.362618000 ## b_gp[8,1] 0.170908512 0.8635115 -1.477259e+00 -0.388029250 ## b_gp[9,1] 0.392874265 0.8290963 -1.195449e+00 -0.126523000 ## b_gp[10,1] -0.178585017 0.8268423 -1.703135e+00 -0.749783250 ## b_gp[11,1] -0.574899302 0.8679366 -2.185671e+00 -1.193132500 ## b_gp[12,1] -0.057668456 0.8223175 -1.784954e+00 -0.613962500 ## b_gp[13,1] 0.494352256 0.9342264 -1.332138e+00 -0.148990750 ## b_gp[14,1] 0.228214400 0.9196630 -1.526855e+00 -0.396093750 ## b_gp[15,1] -0.421532742 0.9248788 -2.201011e+00 -1.037860000 ## b_gp[16,1] -0.135545357 0.9154208 -1.925998e+00 -0.746584750 ## b_gp[17,1] 0.257468256 0.9228638 -1.329210e+00 -0.423805000 ## b_gp[18,1] -0.022888237 0.9102255 -1.740528e+00 -0.565910250 ## b_gp[19,1] -0.259138428 0.9837097 -2.076963e+00 -0.928421000 ## b_gp[20,1] -0.035167617 0.9849405 -1.820254e+00 -0.653108750 ## lambda[1] 41.247648500 17.3247410 1.255886e+01 28.269100000 ## trend[1,1] 0.662344781 0.3696126 -3.455794e-02 0.414853750 ## trend[2,1] 0.691571343 0.3611136 -3.225006e-02 0.463437250 ## trend[3,1] 0.716521468 0.3561785 -4.040503e-03 0.498270750 ## trend[4,1] 0.737052370 0.3542274 -1.260756e-02 0.521204750 ## trend[5,1] 0.753000152 0.3544565 -3.894358e-02 0.548119250 ## trend[6,1] 0.764134909 0.3560572 -6.356761e-02 0.555214250 ## trend[7,1] 0.770132835 0.3583958 -6.201053e-02 0.564625000 ## trend[8,1] 0.770571290 0.3610925 -9.162821e-02 0.570699500 ## trend[9,1] 0.764947719 0.3639779 -1.148054e-01 0.565224250 ## trend[10,1] 0.752724067 0.3669648 -1.574092e-01 0.558487250 ## trend[11,1] 0.733392482 0.3698983 -1.948679e-01 0.537272500 ## trend[12,1] 0.706555268 0.3724615 -2.220962e-01 0.496138750 ## trend[13,1] 0.672012400 0.3741891 -2.470369e-01 0.448868250 ## trend[14,1] 0.629841849 0.3745869 -2.729367e-01 0.415169000 ## trend[15,1] 0.580469751 0.3733240 -2.993852e-01 0.358211500 ## trend[16,1] 0.524711426 0.3704110 -3.365157e-01 0.299569250 ## trend[17,1] 0.463784635 0.3663045 -3.841111e-01 0.233570500 ## trend[18,1] 0.399282235 0.3618687 -4.219333e-01 0.169317250 ## trend[19,1] 0.333108594 0.3581731 -4.633489e-01 0.117502250 ## trend[20,1] 0.267379076 0.3561568 -5.165452e-01 0.050811500 ## trend[21,1] 0.204289996 0.3562734 -5.788225e-01 -0.013071675 ## trend[22,1] 0.145968565 0.3582839 -6.193880e-01 -0.073715750 ## trend[23,1] 0.094314706 0.3613198 -6.884251e-01 -0.124033250 ## trend[24,1] 0.050849235 0.3642022 -7.380625e-01 -0.170861000 ## trend[25,1] 0.016581348 0.3658770 -7.742175e-01 -0.199614250 ## trend[26,1] -0.008090655 0.3658078 -8.029789e-01 -0.220408500 ## trend[27,1] -0.023436432 0.3642155 -7.973271e-01 -0.231379750 ## trend[28,1] -0.030399994 0.3621040 -8.076545e-01 -0.237580750 ## trend[29,1] -0.030553346 0.3610333 -8.026761e-01 -0.250967750 ## trend[30,1] -0.025999765 0.3626414 -8.240066e-01 -0.244710500 ## trend[31,1] -0.019231464 0.3680363 -8.531142e-01 -0.243432000 ## trend[32,1] -0.012953909 0.3773022 -8.817833e-01 -0.248739000 ## trend[33,1] -0.009888287 0.3893868 -9.099955e-01 -0.246213500 ## trend[34,1] -0.012569610 0.4024092 -9.377276e-01 -0.257095000 ## trend[35,1] -0.023155665 0.4141977 -9.649554e-01 -0.274167250 ## trend[36,1] -0.043261835 0.4228099 -9.916493e-01 -0.301634000 ## trend[37,1] -0.073836955 0.4269015 -1.043225e+00 -0.333626750 ## trend[38,1] -0.115087592 0.4259272 -1.071366e+00 -0.367437750 ## trend[39,1] -0.166459676 0.4201980 -1.099210e+00 -0.422837750 ## trend[40,1] -0.226675903 0.4108184 -1.153339e+00 -0.470436500 ## trend[41,1] -0.293827614 0.3995069 -1.181198e+00 -0.529295500 ## trend[42,1] -0.365511123 0.3882883 -1.198303e+00 -0.587900750 ## trend[43,1] -0.438999795 0.3790730 -1.242777e+00 -0.659968750 ## trend[44,1] -0.511434366 0.3731921 -1.292339e+00 -0.737841000 ## trend[45,1] -0.580018731 0.3710561 -1.359167e+00 -0.803339750 ## trend[46,1] -0.642204166 0.3721047 -1.396718e+00 -0.859135000 ## trend[47,1] -0.695848606 0.3750868 -1.422643e+00 -0.917330000 ## trend[48,1] -0.739339646 0.3785248 -1.469708e+00 -0.959464750 ## trend[49,1] -0.771671227 0.3811557 -1.520165e+00 -1.008825000 ## trend[50,1] -0.792473160 0.3822211 -1.540765e+00 -1.023257500 ## trend[51,1] -0.801990394 0.3815739 -1.535978e+00 -1.021197500 ## trend[52,1] -0.801018639 0.3796290 -1.542443e+00 -1.027625000 ## trend[53,1] -0.790801510 0.3771924 -1.541185e+00 -1.011242500 ## trend[54,1] -0.772903223 0.3752137 -1.541188e+00 -0.999957750 ## trend[55,1] -0.749064638 0.3745174 -1.525975e+00 -0.985918750 ## trend[56,1] -0.721060026 0.3755884 -1.536613e+00 -0.952570500 ## trend[57,1] -0.690561937 0.3784756 -1.532405e+00 -0.916547000 ## trend[58,1] -0.659028575 0.3828429 -1.513379e+00 -0.874567250 ## trend[59,1] -0.627618525 0.3881195 -1.496417e+00 -0.839642750 ## trend[60,1] -0.597140890 0.3936819 -1.469950e+00 -0.815878500 ## trend[61,1] -0.568039067 0.3989891 -1.443628e+00 -0.791575500 ## trend[62,1] -0.540410570 0.4036486 -1.421525e+00 -0.769986500 ## trend[63,1] -0.514054636 0.4074130 -1.401414e+00 -0.749367750 ## trend[64,1] -0.488542777 0.4101426 -1.402983e+00 -0.732059750 ## trend[65,1] -0.463304841 0.4117715 -1.400962e+00 -0.701067250 ## trend[66,1] -0.437719328 0.4122954 -1.379707e+00 -0.670499500 ## trend[67,1] -0.411200443 0.4117909 -1.354562e+00 -0.644196750 ## trend[68,1] -0.383274870 0.4104518 -1.335403e+00 -0.629911000 ## trend[69,1] -0.353639451 0.4086142 -1.304757e+00 -0.587006500 ## trend[70,1] -0.322199013 0.4067510 -1.282353e+00 -0.553119250 ## trend[71,1] -0.289079998 0.4054206 -1.228887e+00 -0.520005500 ## trend[72,1] -0.254620962 0.4051796 -1.191347e+00 -0.495036250 ## trend[73,1] -0.219344331 0.4064946 -1.126230e+00 -0.449412750 ## trend[74,1] -0.183910187 0.4096801 -1.099534e+00 -0.425735000 ## trend[75,1] -0.149061908 0.4148909 -1.111180e+00 -0.401606000 ## diag_SPD[1,1] 3.153613966 1.5236433 1.326881e+00 2.114735000 ## diag_SPD[2,1] 2.932903678 1.2037368 1.319392e+00 2.082645000 ## diag_SPD[3,1] 2.644679014 0.9229488 1.295699e+00 2.003880000 ## diag_SPD[4,1] 2.345989042 0.7766457 1.208660e+00 1.826110000 ## diag_SPD[5,1] 2.068087354 0.7388235 7.491192e-01 1.586867500 ## diag_SPD[6,1] 1.822254709 0.7406300 3.109579e-01 1.378827500 ## diag_SPD[7,1] 1.608896941 0.7452507 9.597604e-02 1.195270000 ## diag_SPD[8,1] 1.424380722 0.7435479 2.361056e-02 0.993090500 ## diag_SPD[9,1] 1.264461717 0.7354418 5.066229e-03 0.746482750 ## diag_SPD[10,1] 1.125386775 0.7226702 9.072989e-04 0.569846500 ## diag_SPD[11,1] 1.004053606 0.7069549 1.356267e-04 0.375886250 ## diag_SPD[12,1] 0.897928207 0.6895604 1.691574e-05 0.260405000 ## diag_SPD[13,1] 0.804932273 0.6712602 1.758281e-06 0.172345500 ## diag_SPD[14,1] 0.723339719 0.6524673 1.525762e-07 0.104228100 ## diag_SPD[15,1] 0.651687544 0.6333880 1.105471e-08 0.058485675 ## diag_SPD[16,1] 0.588712421 0.6141381 6.688508e-10 0.034493225 ## diag_SPD[17,1] 0.533308375 0.5948095 3.379890e-11 0.019835600 ## diag_SPD[18,1] 0.484499695 0.5754950 1.426716e-12 0.010823125 ## diag_SPD[19,1] 0.441425830 0.5562939 5.031587e-14 0.005519808 ## diag_SPD[20,1] 0.403329327 0.5373068 1.482801e-15 0.002715183 ## SPD_beta[1,1] -0.223888137 3.1647888 -7.252260e+00 -1.865757500 ## SPD_beta[2,1] 2.785822624 2.0806732 -1.388382e+00 1.580105000 ## SPD_beta[3,1] 1.459537288 2.3885787 -3.216051e+00 -0.029860775 ## SPD_beta[4,1] -2.720070110 1.7833875 -6.332989e+00 -3.853847500 ## SPD_beta[5,1] -1.447226612 1.6531375 -5.303544e+00 -2.435047500 ## SPD_beta[6,1] 1.157670540 1.6307996 -1.747114e+00 0.087216700 ## SPD_beta[7,1] 0.380939892 1.4009691 -2.156009e+00 -0.467801000 ## SPD_beta[8,1] 0.186733053 1.2135526 -2.340948e+00 -0.407824750 ## SPD_beta[9,1] 0.554759553 1.1446236 -1.647484e+00 -0.042748575 ## SPD_beta[10,1] -0.295084479 1.1220540 -2.715458e+00 -0.803267250 ## SPD_beta[11,1] -0.690125797 1.0656534 -3.003994e+00 -1.311022500 ## SPD_beta[12,1] -0.067741477 0.8505043 -2.012086e+00 -0.390429250 ## SPD_beta[13,1] 0.399652206 0.8864740 -1.416712e+00 -0.005982582 ## SPD_beta[14,1] 0.261761889 0.8707224 -1.201241e+00 -0.047004600 ## SPD_beta[15,1] -0.353312930 0.7469753 -2.333371e+00 -0.648996500 ## SPD_beta[16,1] -0.086153326 0.6342989 -1.513623e+00 -0.289598000 ## SPD_beta[17,1] 0.202157698 0.7788614 -1.174562e+00 -0.026247800 ## SPD_beta[18,1] 0.011713697 0.5990158 -1.453137e+00 -0.062246700 ## SPD_beta[19,1] -0.204706346 0.6309776 -1.809440e+00 -0.289615500 ## SPD_beta[20,1] -0.064824950 0.4901487 -1.513491e+00 -0.119507500 ## b[1] 1.008254063 0.3476549 3.808132e-01 0.794186500 ## b[2] -0.364448472 0.1388564 -6.360404e-01 -0.456210750 ## b[3] -0.403166672 0.1692928 -7.333203e-01 -0.504742500 ## b[4] -0.159521633 0.1627585 -4.721557e-01 -0.274457250 ## b[5] 0.170664204 0.1418166 -1.143112e-01 0.075732350 ## b[6] 0.578518208 0.1305816 3.097815e-01 0.494831250 ## b[7] 0.399329137 0.1211636 1.846941e-01 0.314640250 ## mus[1,1] 1.621717482 0.2599556 1.120751e+00 1.435142500 ## mus[2,1] 1.415820670 0.2268869 1.008864e+00 1.253000000 ## mus[3,1] 1.305680328 0.2124920 9.116028e-01 1.154542500 ## mus[4,1] 1.321219594 0.2102551 9.272948e-01 1.180165000 ## mus[5,1] 1.462631436 0.1938968 1.096293e+00 1.336845000 ## mus[6,1] 1.654623760 0.1852974 1.297134e+00 1.528157500 ## mus[7,1] 1.864260600 0.1721239 1.525729e+00 1.747657500 ## mus[8,1] 2.157277760 0.1524800 1.874332e+00 2.049377500 ## mus[9,1] 2.352483660 0.1467176 2.048225e+00 2.258037500 ## mus[10,1] 2.249019320 0.1457346 1.972091e+00 2.151717500 ## mus[11,1] 1.976665080 0.1594537 1.668293e+00 1.864992500 ## mus[12,1] 1.665928400 0.1792588 1.265343e+00 1.546587500 ## mus[13,1] 1.631385160 0.1810574 1.254254e+00 1.508487500 ## mus[14,1] 1.354091344 0.1882438 9.854648e-01 1.224155000 ## mus[15,1] 1.169628830 0.2051507 7.599006e-01 1.033087500 ## mus[16,1] 1.108878352 0.2196305 6.829215e-01 0.973837750 ## mus[17,1] 1.173416016 0.2141108 7.697545e-01 1.020517500 ## mus[18,1] 1.289771284 0.2097707 8.788716e-01 1.161882500 ## mus[19,1] 1.427236540 0.1962091 1.014753e+00 1.301210000 ## mus[20,1] 1.654085760 0.1858490 1.289194e+00 1.546297500 ## mus[21,1] 1.791825720 0.1936082 1.413327e+00 1.674462500 ## mus[22,1] 1.642263920 0.1942632 1.257176e+00 1.524667500 ## mus[23,1] 1.337587554 0.2103633 8.977119e-01 1.196727500 ## mus[24,1] 1.010222132 0.2384182 5.143326e-01 0.854458750 ## mus[25,1] 0.975954064 0.2428561 4.720696e-01 0.825654750 ## mus[26,1] 0.716158531 0.2413754 1.655507e-01 0.563368000 ## mus[27,1] 0.565722538 0.2452160 1.921320e-02 0.410051250 ## mus[28,1] 0.553767153 0.2499344 1.755784e-02 0.403864750 ## mus[29,1] 0.679077927 0.2258193 1.913176e-01 0.544240250 ## mus[30,1] 0.864489232 0.2089806 4.437753e-01 0.731766000 ## mus[31,1] 1.074896682 0.1987097 6.596420e-01 0.945784750 ## mus[32,1] 1.373752508 0.1869564 9.977976e-01 1.241020000 ## mus[33,1] 1.577647220 0.1950440 1.214812e+00 1.439645000 ## mus[34,1] 1.483725780 0.2106536 1.091987e+00 1.330222500 ## mus[35,1] 1.220117182 0.2250224 7.967052e-01 1.057410000 ## mus[36,1] 0.916110808 0.2397768 4.578977e-01 0.748248000 ## mus[37,1] 0.885535858 0.2460571 4.301403e-01 0.717402250 ## mus[38,1] 0.609161609 0.2505920 1.183904e-01 0.424348250 ## mus[39,1] 0.422699301 0.2557363 -2.693525e-02 0.254927500 ## mus[40,1] 0.357491095 0.2542728 -1.288518e-01 0.191007500 ## mus[41,1] 0.415803723 0.2366462 -2.061009e-02 0.259762000 ## mus[42,1] 0.524977863 0.2268496 1.176687e-01 0.370101500 ## mus[43,1] 0.655128126 0.2220103 2.120894e-01 0.490188500 ## mus[44,1] 0.875272240 0.2238374 3.837599e-01 0.737548000 ## mus[45,1] 1.007516960 0.2361360 5.151419e-01 0.868910000 ## mus[46,1] 0.854091071 0.2424020 3.220341e-01 0.701445250 ## mus[47,1] 0.547424072 0.2583912 3.703226e-03 0.392879000 ## mus[48,1] 0.220033118 0.2796128 -3.258178e-01 0.044391725 ## mus[49,1] 0.187701527 0.2863264 -3.897441e-01 0.001282115 ## mus[50,1] -0.068223903 0.2901532 -6.734069e-01 -0.245578250 ## mus[51,1] -0.212831473 0.3028095 -8.436399e-01 -0.396247250 ## mus[52,1] -0.216851610 0.3119836 -8.793085e-01 -0.399580250 ## mus[53,1] -0.081170278 0.2950323 -7.082311e-01 -0.265370000 ## mus[54,1] 0.117585858 0.2801144 -4.368333e-01 -0.072697250 ## mus[55,1] 0.345063392 0.2629482 -2.085769e-01 0.185650500 ## mus[56,1] 0.665646628 0.2441645 1.312509e-01 0.506478750 ## mus[57,1] 0.896973731 0.2415952 3.865160e-01 0.754780250 ## mus[58,1] 0.837266576 0.2416605 3.603397e-01 0.692100000 ## mus[59,1] 0.615654183 0.2394947 1.298245e-01 0.461982750 ## mus[60,1] 0.362231950 0.2410089 -1.274234e-01 0.210850250 ## mus[61,1] 0.391333688 0.2422018 -8.308027e-02 0.231549750 ## mus[62,1] 0.183838612 0.2396150 -2.693150e-01 0.019819675 ## mus[63,1] 0.075104435 0.2501630 -3.923512e-01 -0.096678100 ## mus[64,1] 0.095624329 0.2667455 -4.235836e-01 -0.073080550 ## mus[65,1] 0.246326430 0.2601669 -2.795986e-01 0.065840000 ## mus[66,1] 0.452769654 0.2499609 -3.854166e-02 0.279919500 ## mus[67,1] 0.682927459 0.2372281 1.792977e-01 0.532343000 ## mus[68,1] 1.003431796 0.2263984 5.102642e-01 0.854294250 ## mus[69,1] 1.233896450 0.2273963 7.684105e-01 1.083645000 ## mus[70,1] 1.174096122 0.2191838 7.427018e-01 1.025862500 ## mus[71,1] 0.954192894 0.2160248 5.162897e-01 0.815494250 ## mus[72,1] 0.704751747 0.2310392 2.467365e-01 0.554439000 ## mus[73,1] 0.740028409 0.2466352 2.469223e-01 0.574593750 ## mus[74,1] 0.540339095 0.2777730 -1.350393e-02 0.361976500 ## mus[75,1] 0.440097088 0.3218881 -1.924729e-01 0.215578250 ## rho[1] 3.622159240 0.4627595 2.530289e+00 3.341767500 ## ypred[1,1] 5.258000000 2.6482943 1.000000e+00 3.000000000 ## ypred[2,1] 4.134000000 2.2543754 1.000000e+00 3.000000000 ## ypred[3,1] 3.856000000 2.0687735 1.000000e+00 2.000000000 ## ypred[4,1] 4.018000000 2.2520701 0.000000e+00 2.000000000 ## ypred[5,1] 4.484000000 2.1788158 1.000000e+00 3.000000000 ## ypred[6,1] 5.390000000 2.4807677 1.000000e+00 4.000000000 ## ypred[7,1] 6.512000000 2.7606337 2.000000e+00 5.000000000 ## ypred[8,1] 8.590000000 3.2679135 3.000000e+00 6.000000000 ## ypred[9,1] 10.928000000 3.8637641 4.000000e+00 8.000000000 ## ypred[10,1] 9.436000000 3.6590547 4.000000e+00 7.000000000 ## ypred[11,1] 7.400000000 2.9177090 2.000000e+00 5.000000000 ## ypred[12,1] 5.424000000 2.6041865 1.000000e+00 3.000000000 ## ypred[13,1] 5.282000000 2.4873379 1.000000e+00 4.000000000 ## ypred[14,1] 3.908000000 2.1271072 0.000000e+00 2.000000000 ## ypred[15,1] 3.230000000 1.8729966 0.000000e+00 2.000000000 ## ypred[16,1] 3.040000000 1.8223727 0.000000e+00 2.000000000 ## ypred[17,1] 3.422000000 1.8457328 0.000000e+00 2.000000000 ## ypred[18,1] 3.746000000 2.0093678 0.000000e+00 2.000000000 ## ypred[19,1] 4.272000000 2.2574783 1.000000e+00 3.000000000 ## ypred[20,1] 5.280000000 2.4539037 1.000000e+00 3.000000000 ## ypred[21,1] 6.016000000 2.6762041 1.475000e+00 4.000000000 ## ypred[22,1] 5.214000000 2.4788088 1.000000e+00 3.000000000 ## ypred[23,1] 3.910000000 2.1816092 1.000000e+00 2.000000000 ## ypred[24,1] 2.780000000 1.7691410 0.000000e+00 2.000000000 ## ypred[25,1] 2.708000000 1.7813147 0.000000e+00 1.000000000 ## ypred[26,1] 2.134000000 1.4941583 0.000000e+00 1.000000000 ## ypred[27,1] 1.816000000 1.4457955 0.000000e+00 1.000000000 ## ypred[28,1] 1.754000000 1.4497198 0.000000e+00 1.000000000 ## ypred[29,1] 1.976000000 1.5231757 0.000000e+00 1.000000000 ## ypred[30,1] 2.366000000 1.5584934 0.000000e+00 1.000000000 ## ypred[31,1] 3.008000000 1.7950991 0.000000e+00 2.000000000 ## ypred[32,1] 4.008000000 2.1006574 1.000000e+00 3.000000000 ## ypred[33,1] 4.754000000 2.4276059 1.000000e+00 3.000000000 ## ypred[34,1] 4.602000000 2.3989802 1.000000e+00 3.000000000 ## ypred[35,1] 3.648000000 2.0776741 0.000000e+00 2.000000000 ## ypred[36,1] 2.514000000 1.6767310 0.000000e+00 1.000000000 ## ypred[37,1] 2.480000000 1.7330918 0.000000e+00 1.000000000 ## ypred[38,1] 1.842000000 1.4891175 0.000000e+00 1.000000000 ## ypred[39,1] 1.516000000 1.3165145 0.000000e+00 1.000000000 ## ypred[40,1] 1.432000000 1.2379180 0.000000e+00 1.000000000 ## ypred[41,1] 1.602000000 1.2596704 0.000000e+00 1.000000000 ## ypred[42,1] 1.780000000 1.4253643 0.000000e+00 1.000000000 ## ypred[43,1] 1.910000000 1.4690869 0.000000e+00 1.000000000 ## ypred[44,1] 2.560000000 1.7608524 0.000000e+00 1.000000000 ## ypred[45,1] 2.804000000 1.9070547 0.000000e+00 1.000000000 ## ypred[46,1] 2.520000000 1.6281590 0.000000e+00 1.000000000 ## ypred[47,1] 1.786000000 1.4381727 0.000000e+00 1.000000000 ## ypred[48,1] 1.338000000 1.2958064 0.000000e+00 0.000000000 ## ypred[49,1] 1.332000000 1.2119049 0.000000e+00 0.000000000 ## ypred[50,1] 0.984000000 0.9867580 0.000000e+00 0.000000000 ## ypred[51,1] 0.774000000 0.9255470 0.000000e+00 0.000000000 ## ypred[52,1] 0.818000000 0.9352140 0.000000e+00 0.000000000 ## ypred[53,1] 0.930000000 0.9288841 0.000000e+00 0.000000000 ## ypred[54,1] 1.210000000 1.1386365 0.000000e+00 0.000000000 ## ypred[55,1] 1.544000000 1.2943782 0.000000e+00 1.000000000 ## ypred[56,1] 1.982000000 1.3716555 0.000000e+00 1.000000000 ## ypred[57,1] 2.516000000 1.7039810 0.000000e+00 1.000000000 ## ypred[58,1] 2.404000000 1.7165889 0.000000e+00 1.000000000 ## ypred[59,1] 1.918000000 1.4406342 0.000000e+00 1.000000000 ## ypred[60,1] 1.454000000 1.2787315 0.000000e+00 1.000000000 ## ypred[61,1] 1.592000000 1.2995822 0.000000e+00 1.000000000 ## ypred[62,1] 1.180000000 1.0926976 0.000000e+00 0.000000000 ## ypred[63,1] 1.098000000 1.1040080 0.000000e+00 0.000000000 ## ypred[64,1] 1.202000000 1.1365648 0.000000e+00 0.000000000 ## ypred[65,1] 1.326000000 1.2388679 0.000000e+00 0.000000000 ## ypred[66,1] 1.648000000 1.3985736 0.000000e+00 1.000000000 ## ypred[67,1] 2.054000000 1.4571653 0.000000e+00 1.000000000 ## ypred[68,1] 2.742000000 1.8094154 0.000000e+00 1.000000000 ## ypred[69,1] 3.388000000 2.0053675 0.000000e+00 2.000000000 ## ypred[70,1] 3.406000000 1.9628728 0.000000e+00 2.000000000 ## ypred[71,1] 2.660000000 1.7281125 0.000000e+00 1.000000000 ## ypred[72,1] 2.156000000 1.5750001 0.000000e+00 1.000000000 ## ypred[73,1] 2.252000000 1.6167014 0.000000e+00 1.000000000 ## ypred[74,1] 1.808000000 1.4667784 0.000000e+00 1.000000000 ## ypred[75,1] 1.654000000 1.3393550 0.000000e+00 1.000000000 ## lp__ 67.966422000 4.3759001 5.887928e+01 65.073150000 ## stats ## parameter 50% 75% 97.5% ## alpha_gp[1] 5.750255e-01 0.7217805000 1.040350500 ## rho_gp[1] 1.006590e+01 16.1125500000 35.443937500 ## b_gp[1,1] -8.432960e-02 0.5417947500 1.603338500 ## b_gp[2,1] 1.056340e+00 1.5528650000 2.408657000 ## b_gp[3,1] 5.934650e-01 1.1422625000 2.099837250 ## b_gp[4,1] -1.297740e+00 -0.7513205000 0.362623150 ## b_gp[5,1] -6.812165e-01 -0.1665667500 0.750719775 ## b_gp[6,1] 6.520615e-01 1.1515275000 2.351959750 ## b_gp[7,1] 2.257740e-01 0.7877322500 1.923717250 ## b_gp[8,1] 1.923470e-01 0.7104110000 1.886681500 ## b_gp[9,1] 4.295230e-01 0.8956942500 1.972850750 ## b_gp[10,1] -1.775370e-01 0.3158052500 1.474854250 ## b_gp[11,1] -6.141850e-01 -0.0394184250 1.118444250 ## b_gp[12,1] -3.815655e-02 0.5085745000 1.491042750 ## b_gp[13,1] 5.153470e-01 1.1708425000 2.277357750 ## b_gp[14,1] 2.677425e-01 0.8243945000 1.863428000 ## b_gp[15,1] -4.646090e-01 0.1667100000 1.402041750 ## b_gp[16,1] -1.883570e-01 0.4708485000 1.541283000 ## b_gp[17,1] 2.699740e-01 0.9338577500 2.076618500 ## b_gp[18,1] -3.653185e-02 0.5131182500 1.814965000 ## b_gp[19,1] -3.172720e-01 0.4045230000 1.706570750 ## b_gp[20,1] -3.177160e-02 0.6866040000 1.941039500 ## lambda[1] 3.911650e+01 53.1469000000 79.159317500 ## trend[1,1] 6.590320e-01 0.8962962500 1.398598750 ## trend[2,1] 7.039685e-01 0.9022325000 1.419222750 ## trend[3,1] 7.172335e-01 0.9213642500 1.410105250 ## trend[4,1] 7.450530e-01 0.9395925000 1.422702250 ## trend[5,1] 7.611145e-01 0.9567127500 1.434917500 ## trend[6,1] 7.782110e-01 0.9690157500 1.433527500 ## trend[7,1] 7.801280e-01 0.9824560000 1.435480250 ## trend[8,1] 7.815450e-01 0.9913490000 1.439830000 ## trend[9,1] 7.701620e-01 1.0015050000 1.434023500 ## trend[10,1] 7.587625e-01 0.9926152500 1.422448250 ## trend[11,1] 7.361215e-01 0.9607380000 1.400900750 ## trend[12,1] 7.098850e-01 0.9372415000 1.360377500 ## trend[13,1] 6.696930e-01 0.9066262500 1.324612000 ## trend[14,1] 6.251505e-01 0.8683587500 1.304241250 ## trend[15,1] 5.824525e-01 0.8224247500 1.277645750 ## trend[16,1] 5.379760e-01 0.7595622500 1.227307250 ## trend[17,1] 4.726030e-01 0.6883405000 1.145358000 ## trend[18,1] 4.080115e-01 0.6182015000 1.084233000 ## trend[19,1] 3.314945e-01 0.5517327500 1.038090000 ## trend[20,1] 2.605070e-01 0.4849085000 0.955899150 ## trend[21,1] 2.005640e-01 0.4262710000 0.909974975 ## trend[22,1] 1.397905e-01 0.3720487500 0.860526650 ## trend[23,1] 8.762340e-02 0.3169045000 0.814751150 ## trend[24,1] 4.250145e-02 0.2780305000 0.771730825 ## trend[25,1] 1.163885e-02 0.2465330000 0.729027925 ## trend[26,1] -1.480700e-02 0.2192505000 0.690080650 ## trend[27,1] -2.931495e-02 0.2084372500 0.662099575 ## trend[28,1] -3.357675e-02 0.2036075000 0.653224550 ## trend[29,1] -2.918425e-02 0.1979267500 0.638358625 ## trend[30,1] -2.266055e-02 0.2116265000 0.627323800 ## trend[31,1] -1.198410e-02 0.2132020000 0.634774025 ## trend[32,1] 6.398640e-04 0.2284185000 0.671672925 ## trend[33,1] -5.770085e-03 0.2359940000 0.693282775 ## trend[34,1] 2.709530e-03 0.2467027500 0.723353875 ## trend[35,1] -7.974270e-03 0.2355790000 0.748565000 ## trend[36,1] -1.680185e-02 0.2112425000 0.726114750 ## trend[37,1] -4.671775e-02 0.2011630000 0.700314400 ## trend[38,1] -8.645030e-02 0.1554752500 0.632508475 ## trend[39,1] -1.294765e-01 0.0920736250 0.576475325 ## trend[40,1] -1.904960e-01 0.0372366000 0.475803425 ## trend[41,1] -2.563595e-01 -0.0285595000 0.391461100 ## trend[42,1] -3.325830e-01 -0.1097930000 0.329686425 ## trend[43,1] -4.079725e-01 -0.1845752500 0.247825925 ## trend[44,1] -4.910010e-01 -0.2767082500 0.181379100 ## trend[45,1] -5.772310e-01 -0.3649582500 0.100871660 ## trend[46,1] -6.433150e-01 -0.4145307500 0.064477452 ## trend[47,1] -7.105640e-01 -0.4594802500 0.032421565 ## trend[48,1] -7.573865e-01 -0.4950235000 0.005315812 ## trend[49,1] -7.909535e-01 -0.5405587500 -0.017086633 ## trend[50,1] -8.126080e-01 -0.5631592500 -0.026245998 ## trend[51,1] -8.234485e-01 -0.5665202500 -0.027534298 ## trend[52,1] -8.146330e-01 -0.5685595000 -0.034867804 ## trend[53,1] -8.097800e-01 -0.5649487500 -0.047868730 ## trend[54,1] -7.812465e-01 -0.5518062500 -0.051423070 ## trend[55,1] -7.528010e-01 -0.5272920000 -0.041603058 ## trend[56,1] -7.168030e-01 -0.4763382500 -0.015047985 ## trend[57,1] -6.932105e-01 -0.4577817500 0.021528715 ## trend[58,1] -6.638985e-01 -0.4232012500 0.052465905 ## trend[59,1] -6.373090e-01 -0.3782985000 0.106695490 ## trend[60,1] -6.082605e-01 -0.3471425000 0.183130675 ## trend[61,1] -5.713230e-01 -0.3170005000 0.229741750 ## trend[62,1] -5.382890e-01 -0.2929057500 0.250125825 ## trend[63,1] -5.158085e-01 -0.2596835000 0.272874000 ## trend[64,1] -4.951220e-01 -0.2311417500 0.283851575 ## trend[65,1] -4.681205e-01 -0.2084960000 0.296639900 ## trend[66,1] -4.463420e-01 -0.1858967500 0.310383375 ## trend[67,1] -4.112655e-01 -0.1528515000 0.324353350 ## trend[68,1] -3.762205e-01 -0.1163355000 0.365577675 ## trend[69,1] -3.367650e-01 -0.0984255500 0.397014650 ## trend[70,1] -3.016090e-01 -0.0648958250 0.423029800 ## trend[71,1] -2.780235e-01 -0.0460537750 0.423974525 ## trend[72,1] -2.473385e-01 -0.0085703425 0.442605250 ## trend[73,1] -1.900590e-01 0.0280092250 0.494557950 ## trend[74,1] -1.690315e-01 0.0869629000 0.585881400 ## trend[75,1] -1.296045e-01 0.1359897500 0.641363150 ## diag_SPD[1,1] 2.714615e+00 3.7999000000 7.214828750 ## diag_SPD[2,1] 2.619895e+00 3.5614725000 6.095427000 ## diag_SPD[3,1] 2.459420e+00 3.1276850000 4.714380250 ## diag_SPD[4,1] 2.206270e+00 2.7420475000 4.150187500 ## diag_SPD[5,1] 1.959315e+00 2.4895575000 3.701191500 ## diag_SPD[6,1] 1.801405e+00 2.2929400000 3.361343500 ## diag_SPD[7,1] 1.648995e+00 2.0881400000 3.121447000 ## diag_SPD[8,1] 1.490830e+00 1.8933950000 2.846502000 ## diag_SPD[9,1] 1.318590e+00 1.7342525000 2.669983250 ## diag_SPD[10,1] 1.174785e+00 1.6190050000 2.525051500 ## diag_SPD[11,1] 1.015790e+00 1.5042750000 2.435675250 ## diag_SPD[12,1] 8.769450e-01 1.3575775000 2.355916750 ## diag_SPD[13,1] 7.355765e-01 1.2768300000 2.261330750 ## diag_SPD[14,1] 6.130660e-01 1.1820050000 2.197988750 ## diag_SPD[15,1] 4.888185e-01 1.0644150000 2.112643000 ## diag_SPD[16,1] 4.010690e-01 0.9762192500 2.054339250 ## diag_SPD[17,1] 3.150780e-01 0.9056422500 1.970676000 ## diag_SPD[18,1] 2.503105e-01 0.8037645000 1.896163000 ## diag_SPD[19,1] 1.901380e-01 0.7418615000 1.830646500 ## diag_SPD[20,1] 1.433255e-01 0.6679982500 1.779945500 ## SPD_beta[1,1] -1.997915e-01 1.5114300000 6.331417000 ## SPD_beta[2,1] 2.732210e+00 3.9543825000 7.119167750 ## SPD_beta[3,1] 1.415540e+00 3.0629350000 6.271064500 ## SPD_beta[4,1] -2.666020e+00 -1.7895050000 0.829276625 ## SPD_beta[5,1] -1.331980e+00 -0.3066455000 1.398509500 ## SPD_beta[6,1] 9.924380e-01 2.2911275000 4.375588250 ## SPD_beta[7,1] 2.727315e-01 1.1743450000 3.281979000 ## SPD_beta[8,1] 1.300440e-01 0.8776630000 2.791619250 ## SPD_beta[9,1] 3.801040e-01 1.1161550000 3.247553250 ## SPD_beta[10,1] -3.976900e-02 0.1901857500 1.532220250 ## SPD_beta[11,1] -4.625980e-01 -0.0002071602 1.067125800 ## SPD_beta[12,1] -5.723240e-05 0.2672065000 1.730164500 ## SPD_beta[13,1] 1.226260e-01 0.9019102500 2.406316250 ## SPD_beta[14,1] 2.364840e-02 0.5649980000 2.384457500 ## SPD_beta[15,1] -7.428045e-02 0.0007020165 0.861001925 ## SPD_beta[16,1] -4.391400e-04 0.0704644000 1.320462500 ## SPD_beta[17,1] 9.263750e-04 0.2764800000 2.209004500 ## SPD_beta[18,1] -9.427830e-13 0.1099845000 1.338961000 ## SPD_beta[19,1] -3.599990e-04 0.0088862175 0.705587550 ## SPD_beta[20,1] -3.704180e-15 0.0237075250 0.933152675 ## b[1] 1.016275e+00 1.1887550000 1.811271000 ## b[2] -3.605395e-01 -0.2735065000 -0.085052725 ## b[3] -3.981715e-01 -0.2890032500 -0.080970880 ## b[4] -1.579585e-01 -0.0466510250 0.146811075 ## b[5] 1.776950e-01 0.2718890000 0.423414600 ## b[6] 5.727480e-01 0.6646460000 0.838987150 ## b[7] 3.896160e-01 0.4859682500 0.644479350 ## mus[1,1] 1.626640e+00 1.7980075000 2.111333250 ## mus[2,1] 1.424185e+00 1.5669375000 1.852311500 ## mus[3,1] 1.313455e+00 1.4372675000 1.710501750 ## mus[4,1] 1.310460e+00 1.4594350000 1.740362000 ## mus[5,1] 1.450605e+00 1.5930475000 1.839849000 ## mus[6,1] 1.653080e+00 1.7714000000 2.007018000 ## mus[7,1] 1.862530e+00 1.9817550000 2.198500500 ## mus[8,1] 2.156040e+00 2.2546300000 2.454760000 ## mus[9,1] 2.357535e+00 2.4383850000 2.642418000 ## mus[10,1] 2.246130e+00 2.3463100000 2.547369000 ## mus[11,1] 1.978810e+00 2.0858800000 2.278051250 ## mus[12,1] 1.669475e+00 1.7841050000 2.019766500 ## mus[13,1] 1.631195e+00 1.7480300000 1.990529000 ## mus[14,1] 1.345330e+00 1.4820975000 1.730953250 ## mus[15,1] 1.165425e+00 1.3179825000 1.551906250 ## mus[16,1] 1.108825e+00 1.2611025000 1.507850750 ## mus[17,1] 1.172345e+00 1.3199550000 1.583363250 ## mus[18,1] 1.296165e+00 1.4248950000 1.666443750 ## mus[19,1] 1.439310e+00 1.5510550000 1.771736500 ## mus[20,1] 1.649360e+00 1.7662450000 2.007055250 ## mus[21,1] 1.798020e+00 1.9227100000 2.158539500 ## mus[22,1] 1.646910e+00 1.7838275000 1.984960250 ## mus[23,1] 1.343450e+00 1.4974375000 1.711842500 ## mus[24,1] 1.009155e+00 1.1793550000 1.458811000 ## mus[25,1] 9.803885e-01 1.1501125000 1.418275250 ## mus[26,1] 7.325280e-01 0.8843452500 1.156660000 ## mus[27,1] 5.886380e-01 0.7358620000 1.007321250 ## mus[28,1] 5.726925e-01 0.7283380000 0.990536600 ## mus[29,1] 6.973210e-01 0.8293295000 1.092345250 ## mus[30,1] 8.762555e-01 0.9995355000 1.258926750 ## mus[31,1] 1.086440e+00 1.2115900000 1.439440500 ## mus[32,1] 1.372915e+00 1.5021500000 1.736770000 ## mus[33,1] 1.570375e+00 1.7078525000 1.985585500 ## mus[34,1] 1.461275e+00 1.6161400000 1.918609000 ## mus[35,1] 1.210655e+00 1.3821450000 1.681691000 ## mus[36,1] 9.076485e-01 1.0906250000 1.395238250 ## mus[37,1] 8.692595e-01 1.0595350000 1.392636750 ## mus[38,1] 5.923435e-01 0.7653502500 1.145958250 ## mus[39,1] 4.143900e-01 0.5863660000 0.964559225 ## mus[40,1] 3.642565e-01 0.5164152500 0.861622800 ## mus[41,1] 4.068340e-01 0.5653237500 0.889263125 ## mus[42,1] 5.222610e-01 0.6782630000 0.975222050 ## mus[43,1] 6.637060e-01 0.8024760000 1.111888750 ## mus[44,1] 8.751030e-01 1.0248675000 1.308062500 ## mus[45,1] 1.024590e+00 1.1730225000 1.402734500 ## mus[46,1] 8.722030e-01 1.0259750000 1.249816000 ## mus[47,1] 5.561360e-01 0.7349102500 0.987528475 ## mus[48,1] 2.363055e-01 0.4071482500 0.699338950 ## mus[49,1] 2.087170e-01 0.3881847500 0.655794900 ## mus[50,1] -4.884010e-02 0.1372610000 0.401251350 ## mus[51,1] -1.969305e-01 0.0008286430 0.303908400 ## mus[52,1] -1.948910e-01 -0.0120812675 0.326499650 ## mus[53,1] -4.922900e-02 0.1250227500 0.425606350 ## mus[54,1] 1.367695e-01 0.3035340000 0.617402550 ## mus[55,1] 3.630540e-01 0.5142495000 0.811636650 ## mus[56,1] 6.721935e-01 0.8384255000 1.104479750 ## mus[57,1] 9.062660e-01 1.0644700000 1.328482750 ## mus[58,1] 8.335515e-01 1.0065650000 1.299134250 ## mus[59,1] 6.252875e-01 0.7783785000 1.033918750 ## mus[60,1] 3.651595e-01 0.5116437500 0.808308100 ## mus[61,1] 3.899595e-01 0.5400075000 0.869507175 ## mus[62,1] 1.835745e-01 0.3345082500 0.666296750 ## mus[63,1] 7.443990e-02 0.2444602500 0.581176750 ## mus[64,1] 1.001775e-01 0.2751940000 0.608226375 ## mus[65,1] 2.441000e-01 0.4376280000 0.744390500 ## mus[66,1] 4.653920e-01 0.6322650000 0.932757225 ## mus[67,1] 6.980960e-01 0.8552620000 1.114415250 ## mus[68,1] 1.015085e+00 1.1612850000 1.418485000 ## mus[69,1] 1.233335e+00 1.3795700000 1.663224000 ## mus[70,1] 1.177000e+00 1.3234650000 1.575845000 ## mus[71,1] 9.588800e-01 1.1035650000 1.377680000 ## mus[72,1] 7.212165e-01 0.8679777500 1.127665000 ## mus[73,1] 7.573500e-01 0.9168945000 1.173946500 ## mus[74,1] 5.581595e-01 0.7068797500 1.058995500 ## mus[75,1] 4.274135e-01 0.6594717500 1.097750000 ## rho[1] 3.666540e+00 3.9730575000 4.371423000 ## ypred[1,1] 5.000000e+00 7.0000000000 11.000000000 ## ypred[2,1] 4.000000e+00 5.2500000000 9.000000000 ## ypred[3,1] 4.000000e+00 5.0000000000 8.525000000 ## ypred[4,1] 4.000000e+00 5.0000000000 9.000000000 ## ypred[5,1] 4.000000e+00 6.0000000000 9.525000000 ## ypred[6,1] 5.000000e+00 7.0000000000 10.525000000 ## ypred[7,1] 6.000000e+00 8.0000000000 12.000000000 ## ypred[8,1] 8.000000e+00 11.0000000000 16.000000000 ## ypred[9,1] 1.000000e+01 14.0000000000 19.000000000 ## ypred[10,1] 9.000000e+00 11.2500000000 18.000000000 ## ypred[11,1] 7.000000e+00 9.0000000000 13.000000000 ## ypred[12,1] 5.000000e+00 7.0000000000 11.000000000 ## ypred[13,1] 5.000000e+00 7.0000000000 10.000000000 ## ypred[14,1] 4.000000e+00 5.0000000000 9.000000000 ## ypred[15,1] 3.000000e+00 5.0000000000 7.000000000 ## ypred[16,1] 3.000000e+00 4.0000000000 7.000000000 ## ypred[17,1] 3.000000e+00 5.0000000000 8.000000000 ## ypred[18,1] 4.000000e+00 5.0000000000 8.000000000 ## ypred[19,1] 4.000000e+00 6.0000000000 9.000000000 ## ypred[20,1] 5.000000e+00 7.0000000000 10.000000000 ## ypred[21,1] 6.000000e+00 8.0000000000 11.525000000 ## ypred[22,1] 5.000000e+00 7.0000000000 11.000000000 ## ypred[23,1] 4.000000e+00 5.0000000000 9.000000000 ## ypred[24,1] 3.000000e+00 4.0000000000 6.000000000 ## ypred[25,1] 2.000000e+00 4.0000000000 7.000000000 ## ypred[26,1] 2.000000e+00 3.0000000000 6.000000000 ## ypred[27,1] 2.000000e+00 3.0000000000 5.000000000 ## ypred[28,1] 1.000000e+00 3.0000000000 5.000000000 ## ypred[29,1] 2.000000e+00 3.0000000000 5.000000000 ## ypred[30,1] 2.000000e+00 3.0000000000 6.000000000 ## ypred[31,1] 3.000000e+00 4.0000000000 7.000000000 ## ypred[32,1] 4.000000e+00 5.0000000000 8.000000000 ## ypred[33,1] 4.000000e+00 6.0000000000 10.000000000 ## ypred[34,1] 4.000000e+00 6.0000000000 10.000000000 ## ypred[35,1] 3.000000e+00 5.0000000000 8.000000000 ## ypred[36,1] 2.000000e+00 3.0000000000 6.000000000 ## ypred[37,1] 2.000000e+00 3.0000000000 7.000000000 ## ypred[38,1] 2.000000e+00 3.0000000000 5.000000000 ## ypred[39,1] 1.000000e+00 2.0000000000 5.000000000 ## ypred[40,1] 1.000000e+00 2.0000000000 4.000000000 ## ypred[41,1] 1.000000e+00 2.0000000000 5.000000000 ## ypred[42,1] 2.000000e+00 3.0000000000 5.000000000 ## ypred[43,1] 2.000000e+00 3.0000000000 5.000000000 ## ypred[44,1] 2.000000e+00 3.2500000000 6.000000000 ## ypred[45,1] 2.000000e+00 4.0000000000 7.000000000 ## ypred[46,1] 2.000000e+00 4.0000000000 6.000000000 ## ypred[47,1] 2.000000e+00 3.0000000000 5.000000000 ## ypred[48,1] 1.000000e+00 2.0000000000 5.000000000 ## ypred[49,1] 1.000000e+00 2.0000000000 4.000000000 ## ypred[50,1] 1.000000e+00 2.0000000000 3.000000000 ## ypred[51,1] 1.000000e+00 1.0000000000 3.000000000 ## ypred[52,1] 1.000000e+00 1.0000000000 3.000000000 ## ypred[53,1] 1.000000e+00 1.0000000000 3.000000000 ## ypred[54,1] 1.000000e+00 2.0000000000 4.000000000 ## ypred[55,1] 1.000000e+00 2.0000000000 4.000000000 ## ypred[56,1] 2.000000e+00 3.0000000000 5.000000000 ## ypred[57,1] 2.000000e+00 3.0000000000 7.000000000 ## ypred[58,1] 2.000000e+00 3.0000000000 6.525000000 ## ypred[59,1] 2.000000e+00 3.0000000000 5.000000000 ## ypred[60,1] 1.000000e+00 2.0000000000 4.000000000 ## ypred[61,1] 1.000000e+00 2.0000000000 4.525000000 ## ypred[62,1] 1.000000e+00 2.0000000000 4.000000000 ## ypred[63,1] 1.000000e+00 2.0000000000 4.000000000 ## ypred[64,1] 1.000000e+00 2.0000000000 4.000000000 ## ypred[65,1] 1.000000e+00 2.0000000000 4.000000000 ## ypred[66,1] 1.000000e+00 3.0000000000 5.000000000 ## ypred[67,1] 2.000000e+00 3.0000000000 5.000000000 ## ypred[68,1] 3.000000e+00 4.0000000000 7.000000000 ## ypred[69,1] 3.000000e+00 5.0000000000 8.000000000 ## ypred[70,1] 3.000000e+00 5.0000000000 8.000000000 ## ypred[71,1] 2.500000e+00 4.0000000000 7.000000000 ## ypred[72,1] 2.000000e+00 3.0000000000 6.000000000 ## ypred[73,1] 2.000000e+00 3.0000000000 6.000000000 ## ypred[74,1] 2.000000e+00 3.0000000000 5.000000000 ## ypred[75,1] 1.000000e+00 2.0000000000 4.525000000 ## lp__ 6.803305e+01 71.2243250000 75.633067500 ## ## , , chains = chain:4 ## ## stats ## parameter mean sd 2.5% 25% ## alpha_gp[1] 0.623719348 0.1836247 3.283279e-01 4.877767e-01 ## rho_gp[1] 12.727256620 8.9108522 2.652899e+00 6.919207e+00 ## b_gp[1,1] -0.212916259 0.9231242 -2.069180e+00 -8.623322e-01 ## b_gp[2,1] 0.986341831 0.7605007 -4.526336e-01 4.896855e-01 ## b_gp[3,1] 0.541922117 0.8534587 -1.113772e+00 -4.574653e-02 ## b_gp[4,1] -1.232574611 0.8821894 -3.123604e+00 -1.745633e+00 ## b_gp[5,1] -0.692284664 0.7661083 -2.176804e+00 -1.214247e+00 ## b_gp[6,1] 0.575500683 0.8102735 -1.014705e+00 3.132517e-02 ## b_gp[7,1] 0.248793087 0.8364495 -1.388948e+00 -3.576900e-01 ## b_gp[8,1] 0.112049492 0.7916690 -1.479375e+00 -3.695403e-01 ## b_gp[9,1] 0.337165502 0.8159094 -1.260671e+00 -2.281907e-01 ## b_gp[10,1] -0.183227810 0.8479772 -1.780379e+00 -7.354108e-01 ## b_gp[11,1] -0.526107799 0.9206579 -2.162777e+00 -1.140988e+00 ## b_gp[12,1] -0.040723182 0.8550691 -1.724815e+00 -5.907037e-01 ## b_gp[13,1] 0.494126241 0.9609111 -1.691861e+00 -7.909043e-02 ## b_gp[14,1] 0.174122944 0.9312313 -1.724271e+00 -3.885037e-01 ## b_gp[15,1] -0.341732511 0.9356751 -2.234207e+00 -9.506372e-01 ## b_gp[16,1] -0.123432077 0.9317265 -1.936177e+00 -7.615333e-01 ## b_gp[17,1] 0.361356045 0.9456464 -1.448027e+00 -2.421655e-01 ## b_gp[18,1] 0.122837164 0.9069375 -1.694990e+00 -5.375142e-01 ## b_gp[19,1] -0.186901045 0.9929886 -2.227414e+00 -8.403080e-01 ## b_gp[20,1] 0.012322924 1.0164839 -2.101345e+00 -6.279040e-01 ## lambda[1] 40.479942160 17.7338217 1.072831e+01 2.849405e+01 ## trend[1,1] 0.605883790 0.4010910 -1.629507e-01 3.442580e-01 ## trend[2,1] 0.637028525 0.3903886 -8.008819e-02 3.841117e-01 ## trend[3,1] 0.665435119 0.3826938 -5.488830e-02 4.261640e-01 ## trend[4,1] 0.690603859 0.3782665 -3.943942e-02 4.662803e-01 ## trend[5,1] 0.711935738 0.3768735 -3.543877e-02 4.947023e-01 ## trend[6,1] 0.728730870 0.3778779 -1.369636e-02 5.325878e-01 ## trend[7,1] 0.740205594 0.3804515 -1.076749e-02 5.307715e-01 ## trend[8,1] 0.745529125 0.3837984 -1.685130e-02 5.430778e-01 ## trend[9,1] 0.743876690 0.3872961 -3.455677e-02 5.488237e-01 ## trend[10,1] 0.734498093 0.3905301 -5.927940e-02 5.368635e-01 ## trend[11,1] 0.716794146 0.3932454 -1.129656e-01 4.999970e-01 ## trend[12,1] 0.690395404 0.3952735 -1.540411e-01 4.695360e-01 ## trend[13,1] 0.655235754 0.3964892 -1.840231e-01 4.320483e-01 ## trend[14,1] 0.611611036 0.3968214 -2.157177e-01 3.907925e-01 ## trend[15,1] 0.560217900 0.3963139 -2.488135e-01 3.371102e-01 ## trend[16,1] 0.502163087 0.3951909 -2.830471e-01 2.868108e-01 ## trend[17,1] 0.438943247 0.3938818 -3.173024e-01 2.361535e-01 ## trend[18,1] 0.372389730 0.3929578 -3.582969e-01 1.724518e-01 ## trend[19,1] 0.304583099 0.3929796 -4.076325e-01 9.240717e-02 ## trend[20,1] 0.237738961 0.3942917 -4.623726e-01 1.160945e-02 ## trend[21,1] 0.174074324 0.3968547 -5.117642e-01 -4.885238e-02 ## trend[22,1] 0.115663140 0.4001984 -5.534543e-01 -1.096768e-01 ## trend[23,1] 0.064291658 0.4035357 -5.960736e-01 -1.716422e-01 ## trend[24,1] 0.021325602 0.4060002 -6.563079e-01 -2.145540e-01 ## trend[25,1] -0.012399022 0.4069275 -7.069927e-01 -2.471910e-01 ## trend[26,1] -0.036652171 0.4060909 -7.399799e-01 -2.711768e-01 ## trend[27,1] -0.051845252 0.4038301 -7.604876e-01 -2.850908e-01 ## trend[28,1] -0.059020946 0.4010285 -7.941394e-01 -2.954237e-01 ## trend[29,1] -0.059796038 0.3989279 -8.292443e-01 -2.951030e-01 ## trend[30,1] -0.056260954 0.3987952 -8.793403e-01 -2.924805e-01 ## trend[31,1] -0.050840927 0.4015219 -9.046127e-01 -2.814388e-01 ## trend[32,1] -0.046129366 0.4073046 -9.493131e-01 -2.730097e-01 ## trend[33,1] -0.044705316 0.4155474 -9.856617e-01 -2.882192e-01 ## trend[34,1] -0.048948441 0.4250215 -1.011968e+00 -2.950778e-01 ## trend[35,1] -0.060865644 0.4341995 -1.038610e+00 -3.166647e-01 ## trend[36,1] -0.081943384 0.4416158 -1.063448e+00 -3.408020e-01 ## trend[37,1] -0.113035685 0.4461525 -1.088257e+00 -3.786200e-01 ## trend[38,1] -0.154298574 0.4472146 -1.117684e+00 -4.117140e-01 ## trend[39,1] -0.205174050 0.4448001 -1.147370e+00 -4.788208e-01 ## trend[40,1] -0.264426838 0.4394804 -1.186897e+00 -5.327743e-01 ## trend[41,1] -0.330228448 0.4322982 -1.229683e+00 -5.867915e-01 ## trend[42,1] -0.400284088 0.4245858 -1.288928e+00 -6.267438e-01 ## trend[43,1] -0.471991111 0.4177107 -1.350444e+00 -6.924702e-01 ## trend[44,1] -0.542616444 0.4127818 -1.397178e+00 -7.662583e-01 ## trend[45,1] -0.609479288 0.4103886 -1.473183e+00 -8.370550e-01 ## trend[46,1] -0.670125250 0.4104722 -1.549639e+00 -9.079350e-01 ## trend[47,1] -0.722478656 0.4123890 -1.587042e+00 -9.783975e-01 ## trend[48,1] -0.764961369 0.4151423 -1.627306e+00 -1.018185e+00 ## trend[49,1] -0.796571492 0.4176908 -1.677985e+00 -1.051143e+00 ## trend[50,1] -0.816915769 0.4192252 -1.716790e+00 -1.076900e+00 ## trend[51,1] -0.826194921 0.4193429 -1.724701e+00 -1.085625e+00 ## trend[52,1] -0.825148755 0.4180975 -1.688662e+00 -1.076035e+00 ## trend[53,1] -0.814960944 0.4159250 -1.672467e+00 -1.057410e+00 ## trend[54,1] -0.797138727 0.4134771 -1.649438e+00 -1.052295e+00 ## trend[55,1] -0.773376791 0.4114109 -1.636934e+00 -1.014185e+00 ## trend[56,1] -0.745416127 0.4101955 -1.596455e+00 -9.780237e-01 ## trend[57,1] -0.714911086 0.4100014 -1.553888e+00 -9.555608e-01 ## trend[58,1] -0.683315554 0.4107092 -1.551814e+00 -9.236332e-01 ## trend[59,1] -0.651795942 0.4120166 -1.546445e+00 -8.940512e-01 ## trend[60,1] -0.621176703 0.4135832 -1.536646e+00 -8.621397e-01 ## trend[61,1] -0.591921578 0.4151424 -1.522552e+00 -8.347208e-01 ## trend[62,1] -0.564148781 0.4165363 -1.496040e+00 -8.064375e-01 ## trend[63,1] -0.537677471 0.4176735 -1.454732e+00 -7.775900e-01 ## trend[64,1] -0.512098375 0.4184482 -1.423119e+00 -7.600653e-01 ## trend[65,1] -0.486860429 0.4186815 -1.400000e+00 -7.336037e-01 ## trend[66,1] -0.461364261 0.4181322 -1.363732e+00 -6.944723e-01 ## trend[67,1] -0.435052439 0.4165943 -1.339522e+00 -6.671037e-01 ## trend[68,1] -0.407489130 0.4140521 -1.316240e+00 -6.382235e-01 ## trend[69,1] -0.378420974 0.4108353 -1.285032e+00 -6.132875e-01 ## trend[70,1] -0.347813985 0.4076933 -1.246204e+00 -5.766550e-01 ## trend[71,1] -0.315865263 0.4057304 -1.219035e+00 -5.530080e-01 ## trend[72,1] -0.282988349 0.4061695 -1.201823e+00 -5.274528e-01 ## trend[73,1] -0.249776424 0.4099957 -1.183511e+00 -4.855357e-01 ## trend[74,1] -0.216946475 0.4176148 -1.159556e+00 -4.597615e-01 ## trend[75,1] -0.185271913 0.4287004 -1.122115e+00 -4.360235e-01 ## diag_SPD[1,1] 3.320472680 1.6364730 1.310529e+00 2.116150e+00 ## diag_SPD[2,1] 3.077542000 1.2890380 1.303311e+00 2.067925e+00 ## diag_SPD[3,1] 2.762280800 0.9958880 1.283454e+00 1.990448e+00 ## diag_SPD[4,1] 2.441948058 0.8650525 1.117464e+00 1.838835e+00 ## diag_SPD[5,1] 2.150219711 0.8333905 5.610850e-01 1.607860e+00 ## diag_SPD[6,1] 1.895130648 0.8245296 1.840065e-01 1.412422e+00 ## diag_SPD[7,1] 1.673761494 0.8104741 4.599790e-02 1.249780e+00 ## diag_SPD[8,1] 1.480824532 0.7871224 1.009419e-02 1.022977e+00 ## diag_SPD[9,1] 1.311586513 0.7569291 1.670237e-03 8.330975e-01 ## diag_SPD[10,1] 1.162371800 0.7233226 2.202841e-04 6.242353e-01 ## diag_SPD[11,1] 1.030411620 0.6890319 2.348279e-05 4.651677e-01 ## diag_SPD[12,1] 0.913595463 0.6557270 2.078755e-06 3.216507e-01 ## diag_SPD[13,1] 0.810245169 0.6241764 1.508517e-07 2.166762e-01 ## diag_SPD[14,1] 0.718951059 0.5945644 8.879361e-09 1.330398e-01 ## diag_SPD[15,1] 0.638468586 0.5667794 4.239853e-10 7.992520e-02 ## diag_SPD[16,1] 0.567657800 0.5406037 1.642538e-11 4.583132e-02 ## diag_SPD[17,1] 0.505461778 0.5158219 5.163365e-13 2.554353e-02 ## diag_SPD[18,1] 0.450897324 0.4922580 1.315886e-14 1.382410e-02 ## diag_SPD[19,1] 0.403056963 0.4697837 2.716159e-16 7.223660e-03 ## diag_SPD[20,1] 0.361112668 0.4483123 4.550658e-18 3.644560e-03 ## SPD_beta[1,1] -0.581763570 3.5750263 -7.909085e+00 -2.430203e+00 ## SPD_beta[2,1] 2.805256175 2.3731496 -1.850272e+00 1.244540e+00 ## SPD_beta[3,1] 1.392110199 2.4230332 -3.226357e+00 -1.190023e-01 ## SPD_beta[4,1] -2.723869668 2.0810541 -6.817750e+00 -3.988923e+00 ## SPD_beta[5,1] -1.399137707 1.6434734 -4.711989e+00 -2.469835e+00 ## SPD_beta[6,1] 1.118064887 1.6928162 -1.869472e+00 2.143027e-02 ## SPD_beta[7,1] 0.440126982 1.4284465 -2.022812e+00 -3.933032e-01 ## SPD_beta[8,1] 0.209096357 1.2768268 -2.442503e+00 -4.539127e-01 ## SPD_beta[9,1] 0.518903633 1.1783506 -1.768461e+00 -7.899995e-02 ## SPD_beta[10,1] -0.217475996 1.0999941 -2.541631e+00 -7.298680e-01 ## SPD_beta[11,1] -0.621116434 1.0546712 -2.841185e+00 -1.201002e+00 ## SPD_beta[12,1] -0.037144457 0.8807043 -1.901968e+00 -4.306138e-01 ## SPD_beta[13,1] 0.513838912 0.8762034 -8.440506e-01 -1.194892e-05 ## SPD_beta[14,1] 0.194098098 0.7648364 -1.070475e+00 -8.524437e-02 ## SPD_beta[15,1] -0.271655397 0.6852820 -1.975471e+00 -5.285902e-01 ## SPD_beta[16,1] -0.105963253 0.6250628 -1.500907e+00 -2.833775e-01 ## SPD_beta[17,1] 0.259753821 0.6723128 -7.894127e-01 -1.466232e-03 ## SPD_beta[18,1] 0.098072665 0.5945197 -1.077548e+00 -3.854285e-02 ## SPD_beta[19,1] -0.143874643 0.5572516 -1.569473e+00 -2.288015e-01 ## SPD_beta[20,1] -0.009344612 0.5360500 -1.112953e+00 -6.716350e-02 ## b[1] 1.041990590 0.3709027 3.171200e-01 8.197237e-01 ## b[2] -0.354434495 0.1520672 -6.612493e-01 -4.544965e-01 ## b[3] -0.396558451 0.1668895 -7.362621e-01 -5.075355e-01 ## b[4] -0.162045368 0.1657816 -4.928461e-01 -2.717967e-01 ## b[5] 0.145136958 0.1389640 -1.134523e-01 4.967027e-02 ## b[6] 0.566294722 0.1429365 2.985929e-01 4.578118e-01 ## b[7] 0.402909305 0.1316494 1.444116e-01 3.125142e-01 ## mus[1,1] 1.604933964 0.2789197 9.827270e-01 1.432653e+00 ## mus[2,1] 1.404761920 0.2440910 8.859811e-01 1.242563e+00 ## mus[3,1] 1.299644914 0.2205637 8.483300e-01 1.170325e+00 ## mus[4,1] 1.316818672 0.2118185 8.820167e-01 1.170548e+00 ## mus[5,1] 1.460260650 0.2020321 1.063481e+00 1.330248e+00 ## mus[6,1] 1.647282400 0.1965784 1.244931e+00 1.515262e+00 ## mus[7,1] 1.846111400 0.1708610 1.510454e+00 1.727943e+00 ## mus[8,1] 2.143908100 0.1588266 1.814038e+00 2.036503e+00 ## mus[9,1] 2.356131540 0.1753087 2.006125e+00 2.234095e+00 ## mus[10,1] 2.266694940 0.1682534 1.919871e+00 2.152782e+00 ## mus[11,1] 1.999640560 0.1621401 1.680862e+00 1.890457e+00 ## mus[12,1] 1.689445660 0.1683611 1.371071e+00 1.574920e+00 ## mus[13,1] 1.654285800 0.1686649 1.323678e+00 1.544685e+00 ## mus[14,1] 1.379344360 0.1919420 1.009314e+00 1.249998e+00 ## mus[15,1] 1.194427542 0.2135801 7.564419e-01 1.058400e+00 ## mus[16,1] 1.128377862 0.2191471 7.026711e-01 9.883322e-01 ## mus[17,1] 1.187268142 0.2109327 7.690417e-01 1.046395e+00 ## mus[18,1] 1.290941188 0.2158494 8.492815e-01 1.144565e+00 ## mus[19,1] 1.410488756 0.2068640 1.005527e+00 1.269730e+00 ## mus[20,1] 1.636118150 0.1980465 1.237564e+00 1.502220e+00 ## mus[21,1] 1.786328860 0.2127484 1.369038e+00 1.643830e+00 ## mus[22,1] 1.647859680 0.2206331 1.203573e+00 1.500165e+00 ## mus[23,1] 1.347138124 0.2249784 8.678022e-01 1.192745e+00 ## mus[24,1] 1.020375658 0.2304960 5.319704e-01 8.784415e-01 ## mus[25,1] 0.986651166 0.2331413 5.065898e-01 8.473548e-01 ## mus[26,1] 0.731081053 0.2487979 2.047869e-01 5.838678e-01 ## mus[27,1] 0.582364458 0.2578724 6.078636e-03 4.097655e-01 ## mus[28,1] 0.567193893 0.2482571 6.938445e-02 4.012390e-01 ## mus[29,1] 0.688529083 0.2306988 2.230013e-01 5.468750e-01 ## mus[30,1] 0.862290444 0.2266632 3.850016e-01 7.234760e-01 ## mus[31,1] 1.055064940 0.2059453 6.687095e-01 9.067057e-01 ## mus[32,1] 1.352249658 0.1890082 9.883978e-01 1.223372e+00 ## mus[33,1] 1.567549102 0.2059732 1.134486e+00 1.431338e+00 ## mus[34,1] 1.483248448 0.2150033 1.055443e+00 1.346035e+00 ## mus[35,1] 1.221980780 0.2186507 7.813620e-01 1.074950e+00 ## mus[36,1] 0.917106960 0.2268889 4.709904e-01 7.684647e-01 ## mus[37,1] 0.886014388 0.2325275 4.357546e-01 7.315095e-01 ## mus[38,1] 0.613434753 0.2482807 1.383805e-01 4.408323e-01 ## mus[39,1] 0.429035642 0.2608605 -5.467098e-02 2.524108e-01 ## mus[40,1] 0.361787911 0.2623357 -1.093046e-01 1.930050e-01 ## mus[41,1] 0.418096631 0.2503331 -8.406061e-02 2.534413e-01 ## mus[42,1] 0.518267314 0.2430832 3.697949e-02 3.681505e-01 ## mus[43,1] 0.633914590 0.2256811 1.982116e-01 4.894915e-01 ## mus[44,1] 0.855762579 0.2237145 4.169385e-01 7.042415e-01 ## mus[45,1] 1.002775404 0.2462618 5.235596e-01 8.301953e-01 ## mus[46,1] 0.862071466 0.2513219 3.524179e-01 6.966672e-01 ## mus[47,1] 0.560367871 0.2546326 2.604917e-02 4.027705e-01 ## mus[48,1] 0.234088781 0.2648118 -2.985058e-01 5.705983e-02 ## mus[49,1] 0.202478602 0.2752577 -3.717440e-01 1.746372e-02 ## mus[50,1] -0.049182450 0.2897563 -6.814398e-01 -2.164280e-01 ## mus[51,1] -0.191985263 0.3009434 -8.501468e-01 -3.706595e-01 ## mus[52,1] -0.198934027 0.3029777 -8.202203e-01 -3.969375e-01 ## mus[53,1] -0.066635830 0.2922480 -6.544149e-01 -2.418962e-01 ## mus[54,1] 0.121412701 0.2829346 -4.951336e-01 -6.208223e-02 ## mus[55,1] 0.332528896 0.2581544 -2.390401e-01 1.707900e-01 ## mus[56,1] 0.652962929 0.2417732 1.718102e-01 4.989435e-01 ## mus[57,1] 0.897343702 0.2464120 4.120816e-01 7.407307e-01 ## mus[58,1] 0.848881059 0.2347768 3.700353e-01 6.915483e-01 ## mus[59,1] 0.631050484 0.2251951 1.796470e-01 4.922175e-01 ## mus[60,1] 0.377873362 0.2240638 -5.759511e-02 2.376825e-01 ## mus[61,1] 0.407128490 0.2197971 -2.885251e-02 2.721807e-01 ## mus[62,1] 0.203584365 0.2340133 -2.331726e-01 4.705803e-02 ## mus[63,1] 0.096532208 0.2527042 -3.662113e-01 -9.365087e-02 ## mus[64,1] 0.114116405 0.2592815 -3.827012e-01 -6.476540e-02 ## mus[65,1] 0.261464619 0.2528486 -2.317654e-01 8.517627e-02 ## mus[66,1] 0.457187201 0.2556413 -6.052899e-02 2.908020e-01 ## mus[67,1] 0.670853331 0.2427646 1.464335e-01 5.266892e-01 ## mus[68,1] 0.990889788 0.2240175 5.113353e-01 8.539163e-01 ## mus[69,1] 1.233833620 0.2239167 7.620453e-01 1.084893e+00 ## mus[70,1] 1.184382722 0.2246934 7.500487e-01 1.032728e+00 ## mus[71,1] 0.966981156 0.2302371 5.227972e-01 8.241010e-01 ## mus[72,1] 0.716061798 0.2419015 2.481288e-01 5.562565e-01 ## mus[73,1] 0.749273778 0.2617287 2.228599e-01 5.736923e-01 ## mus[74,1] 0.550786764 0.2850312 -3.967319e-03 3.655570e-01 ## mus[75,1] 0.448937761 0.3169974 -2.032719e-01 2.530845e-01 ## rho[1] 3.595742240 0.4835477 2.372827e+00 3.349695e+00 ## ypred[1,1] 5.300000000 2.6152781 1.000000e+00 3.000000e+00 ## ypred[2,1] 4.220000000 2.3061302 1.000000e+00 3.000000e+00 ## ypred[3,1] 3.792000000 2.0979845 1.000000e+00 2.000000e+00 ## ypred[4,1] 3.800000000 2.0347679 0.000000e+00 2.000000e+00 ## ypred[5,1] 4.316000000 2.2721067 1.000000e+00 3.000000e+00 ## ypred[6,1] 5.308000000 2.5632551 1.000000e+00 3.000000e+00 ## ypred[7,1] 6.384000000 2.7828101 2.000000e+00 4.000000e+00 ## ypred[8,1] 8.616000000 3.4076044 3.000000e+00 6.000000e+00 ## ypred[9,1] 10.750000000 3.8105828 5.000000e+00 8.000000e+00 ## ypred[10,1] 9.798000000 3.6413892 4.000000e+00 7.000000e+00 ## ypred[11,1] 7.510000000 2.9906166 2.475000e+00 5.000000e+00 ## ypred[12,1] 5.540000000 2.5260963 1.000000e+00 4.000000e+00 ## ypred[13,1] 5.274000000 2.3770201 1.000000e+00 4.000000e+00 ## ypred[14,1] 4.320000000 2.2493820 4.750000e-01 3.000000e+00 ## ypred[15,1] 3.332000000 1.9527936 0.000000e+00 2.000000e+00 ## ypred[16,1] 3.176000000 1.8590148 0.000000e+00 2.000000e+00 ## ypred[17,1] 3.314000000 1.8434208 0.000000e+00 2.000000e+00 ## ypred[18,1] 3.666000000 2.1079209 0.000000e+00 2.000000e+00 ## ypred[19,1] 4.182000000 2.1489793 1.000000e+00 3.000000e+00 ## ypred[20,1] 5.272000000 2.5469570 1.000000e+00 3.000000e+00 ## ypred[21,1] 6.132000000 2.7629411 1.000000e+00 4.000000e+00 ## ypred[22,1] 5.198000000 2.7043341 1.000000e+00 3.000000e+00 ## ypred[23,1] 3.872000000 2.2157245 0.000000e+00 2.000000e+00 ## ypred[24,1] 2.992000000 1.8260901 0.000000e+00 2.000000e+00 ## ypred[25,1] 2.604000000 1.6926056 0.000000e+00 1.000000e+00 ## ypred[26,1] 2.218000000 1.4936324 0.000000e+00 1.000000e+00 ## ypred[27,1] 1.724000000 1.4422150 0.000000e+00 1.000000e+00 ## ypred[28,1] 1.750000000 1.4069324 0.000000e+00 1.000000e+00 ## ypred[29,1] 2.064000000 1.5220174 0.000000e+00 1.000000e+00 ## ypred[30,1] 2.456000000 1.8414249 0.000000e+00 1.000000e+00 ## ypred[31,1] 2.898000000 1.7611927 0.000000e+00 2.000000e+00 ## ypred[32,1] 3.886000000 2.0211814 0.000000e+00 2.000000e+00 ## ypred[33,1] 4.898000000 2.4819178 1.000000e+00 3.000000e+00 ## ypred[34,1] 4.746000000 2.3281591 1.000000e+00 3.000000e+00 ## ypred[35,1] 3.426000000 1.9657702 0.000000e+00 2.000000e+00 ## ypred[36,1] 2.530000000 1.6463660 0.000000e+00 1.000000e+00 ## ypred[37,1] 2.484000000 1.6598959 0.000000e+00 1.000000e+00 ## ypred[38,1] 1.892000000 1.3986595 0.000000e+00 1.000000e+00 ## ypred[39,1] 1.576000000 1.4861498 0.000000e+00 1.000000e+00 ## ypred[40,1] 1.408000000 1.2572579 0.000000e+00 0.000000e+00 ## ypred[41,1] 1.686000000 1.3868131 0.000000e+00 1.000000e+00 ## ypred[42,1] 1.650000000 1.3781504 0.000000e+00 1.000000e+00 ## ypred[43,1] 2.032000000 1.5058257 0.000000e+00 1.000000e+00 ## ypred[44,1] 2.390000000 1.6009454 0.000000e+00 1.000000e+00 ## ypred[45,1] 2.708000000 1.7722917 0.000000e+00 1.000000e+00 ## ypred[46,1] 2.514000000 1.7227128 0.000000e+00 1.000000e+00 ## ypred[47,1] 1.784000000 1.4075889 0.000000e+00 1.000000e+00 ## ypred[48,1] 1.398000000 1.2290717 0.000000e+00 0.000000e+00 ## ypred[49,1] 1.298000000 1.2017005 0.000000e+00 0.000000e+00 ## ypred[50,1] 1.028000000 1.0796051 0.000000e+00 0.000000e+00 ## ypred[51,1] 0.806000000 0.8542972 0.000000e+00 0.000000e+00 ## ypred[52,1] 0.906000000 0.9607341 0.000000e+00 0.000000e+00 ## ypred[53,1] 0.998000000 1.0640773 0.000000e+00 0.000000e+00 ## ypred[54,1] 1.208000000 1.1642366 0.000000e+00 0.000000e+00 ## ypred[55,1] 1.410000000 1.2397475 0.000000e+00 0.000000e+00 ## ypred[56,1] 1.980000000 1.4532115 0.000000e+00 1.000000e+00 ## ypred[57,1] 2.518000000 1.7086588 0.000000e+00 1.000000e+00 ## ypred[58,1] 2.394000000 1.6493042 0.000000e+00 1.000000e+00 ## ypred[59,1] 1.948000000 1.4579256 0.000000e+00 1.000000e+00 ## ypred[60,1] 1.506000000 1.2316647 0.000000e+00 1.000000e+00 ## ypred[61,1] 1.540000000 1.2423715 0.000000e+00 1.000000e+00 ## ypred[62,1] 1.238000000 1.2084190 0.000000e+00 0.000000e+00 ## ypred[63,1] 1.132000000 1.1336429 0.000000e+00 0.000000e+00 ## ypred[64,1] 1.166000000 1.2204191 0.000000e+00 0.000000e+00 ## ypred[65,1] 1.360000000 1.1511082 0.000000e+00 0.000000e+00 ## ypred[66,1] 1.578000000 1.4070806 0.000000e+00 1.000000e+00 ## ypred[67,1] 2.026000000 1.5653193 0.000000e+00 1.000000e+00 ## ypred[68,1] 2.736000000 1.8658152 0.000000e+00 1.000000e+00 ## ypred[69,1] 3.622000000 2.1382845 0.000000e+00 2.000000e+00 ## ypred[70,1] 3.240000000 2.0244992 0.000000e+00 2.000000e+00 ## ypred[71,1] 2.708000000 1.8103289 0.000000e+00 1.000000e+00 ## ypred[72,1] 2.076000000 1.4360880 0.000000e+00 1.000000e+00 ## ypred[73,1] 2.256000000 1.6709423 0.000000e+00 1.000000e+00 ## ypred[74,1] 1.794000000 1.4126412 0.000000e+00 1.000000e+00 ## ypred[75,1] 1.622000000 1.4502836 0.000000e+00 1.000000e+00 ## lp__ 67.423765400 4.8728039 5.726290e+01 6.429010e+01 ## stats ## parameter 50% 75% 97.5% ## alpha_gp[1] 5.958730e-01 0.7407622500 1.006014750 ## rho_gp[1] 9.753410e+00 15.5867750000 38.144887500 ## b_gp[1,1] -1.829180e-01 0.3836205000 1.507362000 ## b_gp[2,1] 9.710530e-01 1.5318150000 2.457062750 ## b_gp[3,1] 5.583430e-01 1.0978125000 2.227414500 ## b_gp[4,1] -1.174935e+00 -0.6553967500 0.562308025 ## b_gp[5,1] -7.270345e-01 -0.2056230000 0.812967450 ## b_gp[6,1] 5.675305e-01 1.1181425000 2.174640750 ## b_gp[7,1] 3.217535e-01 0.8631520000 1.685393500 ## b_gp[8,1] 1.209245e-01 0.6563370000 1.618529250 ## b_gp[9,1] 4.071445e-01 0.8963417500 1.840179750 ## b_gp[10,1] -2.195875e-01 0.3278755000 1.414533500 ## b_gp[11,1] -5.858350e-01 0.0760276500 1.362795250 ## b_gp[12,1] -1.048930e-01 0.5111760000 1.768527000 ## b_gp[13,1] 5.123560e-01 1.0592125000 2.409820000 ## b_gp[14,1] 1.456325e-01 0.8037592500 2.011810500 ## b_gp[15,1] -3.451420e-01 0.2163405000 1.484895250 ## b_gp[16,1] -9.510710e-02 0.4948242500 1.730166000 ## b_gp[17,1] 3.700365e-01 1.0052325000 2.083567500 ## b_gp[18,1] 1.617705e-01 0.7736012500 1.892119000 ## b_gp[19,1] -1.660065e-01 0.4670645000 1.916968750 ## b_gp[20,1] 2.421260e-02 0.5958980000 2.061907500 ## lambda[1] 3.860600e+01 50.9582500000 79.314210000 ## trend[1,1] 6.180345e-01 0.8236155000 1.508103750 ## trend[2,1] 6.466320e-01 0.8564380000 1.470285750 ## trend[3,1] 6.731125e-01 0.8852522500 1.503034500 ## trend[4,1] 6.915725e-01 0.9053330000 1.526363750 ## trend[5,1] 7.074400e-01 0.9262762500 1.505750500 ## trend[6,1] 7.219785e-01 0.9473200000 1.503114000 ## trend[7,1] 7.264980e-01 0.9605947500 1.487407500 ## trend[8,1] 7.383040e-01 0.9649745000 1.464882000 ## trend[9,1] 7.534335e-01 0.9707650000 1.449230500 ## trend[10,1] 7.512215e-01 0.9717320000 1.445196500 ## trend[11,1] 7.291635e-01 0.9458630000 1.462034000 ## trend[12,1] 6.948205e-01 0.9286330000 1.464406250 ## trend[13,1] 6.691920e-01 0.8836650000 1.443353750 ## trend[14,1] 6.307380e-01 0.8333832500 1.401136750 ## trend[15,1] 5.761820e-01 0.7737462500 1.362045250 ## trend[16,1] 5.137240e-01 0.7128757500 1.337180500 ## trend[17,1] 4.456430e-01 0.6456450000 1.298083250 ## trend[18,1] 3.694100e-01 0.5669205000 1.246831000 ## trend[19,1] 2.997855e-01 0.5016005000 1.179017750 ## trend[20,1] 2.294040e-01 0.4437845000 1.114485500 ## trend[21,1] 1.586885e-01 0.3778362500 1.067422500 ## trend[22,1] 1.066860e-01 0.3127632500 1.023597850 ## trend[23,1] 4.042815e-02 0.2577482500 0.978725575 ## trend[24,1] -6.766720e-03 0.2195442500 0.931647650 ## trend[25,1] -4.332950e-02 0.2054030000 0.881799650 ## trend[26,1] -5.650495e-02 0.1817637500 0.832225050 ## trend[27,1] -7.445350e-02 0.1712622500 0.808123075 ## trend[28,1] -8.333265e-02 0.1659287500 0.757625300 ## trend[29,1] -8.097100e-02 0.1590092500 0.713454850 ## trend[30,1] -6.081810e-02 0.1697320000 0.728913900 ## trend[31,1] -4.018705e-02 0.1769230000 0.772639550 ## trend[32,1] -2.857135e-02 0.1875382500 0.808430275 ## trend[33,1] -2.180550e-02 0.2068255000 0.832262175 ## trend[34,1] -2.277355e-02 0.2048575000 0.809044950 ## trend[35,1] -2.627500e-02 0.1920207500 0.779961175 ## trend[36,1] -5.012655e-02 0.1879900000 0.748036700 ## trend[37,1] -7.951290e-02 0.1660697500 0.721477475 ## trend[38,1] -1.295820e-01 0.1198200000 0.693913300 ## trend[39,1] -1.753850e-01 0.0610074250 0.654190150 ## trend[40,1] -2.308045e-01 0.0026865600 0.597884550 ## trend[41,1] -2.952170e-01 -0.0570900000 0.522021725 ## trend[42,1] -3.681235e-01 -0.1509412500 0.462412150 ## trend[43,1] -4.571080e-01 -0.2410082500 0.391464925 ## trend[44,1] -5.319055e-01 -0.3052160000 0.328008450 ## trend[45,1] -6.025090e-01 -0.3503572500 0.263285375 ## trend[46,1] -6.604425e-01 -0.4190242500 0.199294225 ## trend[47,1] -7.225200e-01 -0.4809245000 0.141348225 ## trend[48,1] -7.753025e-01 -0.5267572500 0.091034272 ## trend[49,1] -8.002235e-01 -0.5516222500 0.064543377 ## trend[50,1] -8.095845e-01 -0.5679502500 0.044781197 ## trend[51,1] -8.152280e-01 -0.5701975000 0.023085360 ## trend[52,1] -8.087010e-01 -0.5651715000 -0.001465204 ## trend[53,1] -7.971915e-01 -0.5605477500 -0.017433330 ## trend[54,1] -7.753295e-01 -0.5453735000 -0.026781395 ## trend[55,1] -7.505385e-01 -0.5232662500 -0.023063208 ## trend[56,1] -7.188545e-01 -0.4929927500 0.003735927 ## trend[57,1] -6.829510e-01 -0.4543317500 0.027188508 ## trend[58,1] -6.432810e-01 -0.4267725000 0.035848775 ## trend[59,1] -6.161600e-01 -0.3973542500 0.045884455 ## trend[60,1] -5.816140e-01 -0.3685895000 0.110457200 ## trend[61,1] -5.673300e-01 -0.3480640000 0.163925900 ## trend[62,1] -5.440880e-01 -0.3077407500 0.214132850 ## trend[63,1] -5.209570e-01 -0.2769587500 0.271995375 ## trend[64,1] -4.916515e-01 -0.2541257500 0.301209125 ## trend[65,1] -4.672695e-01 -0.2256907500 0.345218400 ## trend[66,1] -4.450500e-01 -0.2024130000 0.369497075 ## trend[67,1] -4.243465e-01 -0.1880370000 0.344597925 ## trend[68,1] -3.920180e-01 -0.1677987500 0.340998500 ## trend[69,1] -3.565150e-01 -0.1377872500 0.353455900 ## trend[70,1] -3.209665e-01 -0.0986948000 0.371827700 ## trend[71,1] -2.719080e-01 -0.0803054250 0.401094475 ## trend[72,1] -2.405430e-01 -0.0419856750 0.481581975 ## trend[73,1] -2.163175e-01 -0.0096643200 0.523283500 ## trend[74,1] -2.011925e-01 0.0423413000 0.568620525 ## trend[75,1] -1.760595e-01 0.0813584500 0.661252925 ## diag_SPD[1,1] 2.884205e+00 4.1299725000 7.795085000 ## diag_SPD[2,1] 2.779475e+00 3.8653475000 6.068271500 ## diag_SPD[3,1] 2.602895e+00 3.4816275000 4.950104000 ## diag_SPD[4,1] 2.318720e+00 2.9607375000 4.446244500 ## diag_SPD[5,1] 2.037185e+00 2.6563525000 3.943311250 ## diag_SPD[6,1] 1.843290e+00 2.3426900000 3.587038000 ## diag_SPD[7,1] 1.674110e+00 2.1446150000 3.275507750 ## diag_SPD[8,1] 1.517880e+00 1.9752575000 2.961868250 ## diag_SPD[9,1] 1.390315e+00 1.8081775000 2.690981000 ## diag_SPD[10,1] 1.255500e+00 1.6370775000 2.504716500 ## diag_SPD[11,1] 1.122735e+00 1.4949675000 2.370236250 ## diag_SPD[12,1] 9.844105e-01 1.3700475000 2.240588500 ## diag_SPD[13,1] 8.445025e-01 1.2538350000 2.074883000 ## diag_SPD[14,1] 7.038275e-01 1.1308200000 1.937732000 ## diag_SPD[15,1] 5.666395e-01 1.0362100000 1.850906250 ## diag_SPD[16,1] 4.626295e-01 0.9330557500 1.756705250 ## diag_SPD[17,1] 3.752525e-01 0.8493520000 1.675164750 ## diag_SPD[18,1] 2.995830e-01 0.7448645000 1.624117750 ## diag_SPD[19,1] 2.308825e-01 0.6751570000 1.555283750 ## diag_SPD[20,1] 1.747380e-01 0.5980237500 1.487341500 ## SPD_beta[1,1] -5.170540e-01 1.0019750000 6.655190500 ## SPD_beta[2,1] 2.670745e+00 4.2265200000 7.886388250 ## SPD_beta[3,1] 1.246890e+00 2.7591475000 6.739336000 ## SPD_beta[4,1] -2.602395e+00 -1.5040800000 1.457271000 ## SPD_beta[5,1] -1.303720e+00 -0.3544760000 1.754967250 ## SPD_beta[6,1] 8.885995e-01 2.0998225000 4.971913500 ## SPD_beta[7,1] 2.768225e-01 1.2390075000 3.673505500 ## SPD_beta[8,1] 8.168115e-02 0.7792617500 2.887624000 ## SPD_beta[9,1] 3.353315e-01 1.1871075000 2.971061000 ## SPD_beta[10,1] -7.301545e-02 0.2212682500 2.156658250 ## SPD_beta[11,1] -3.800745e-01 0.0008433085 1.103572000 ## SPD_beta[12,1] -4.968440e-05 0.3038112500 2.118231500 ## SPD_beta[13,1] 2.880185e-01 0.9002405000 2.637039750 ## SPD_beta[14,1] 3.811475e-03 0.4635855000 2.018890750 ## SPD_beta[15,1] -4.328260e-02 0.0036161150 0.872409775 ## SPD_beta[16,1] -5.536795e-05 0.0793536500 1.078061750 ## SPD_beta[17,1] 1.747420e-02 0.4326705000 2.024790000 ## SPD_beta[18,1] 7.921835e-06 0.2277950000 1.485518000 ## SPD_beta[19,1] -2.230925e-05 0.0171277750 0.770068975 ## SPD_beta[20,1] 5.580940e-19 0.0542744000 0.867058800 ## b[1] 1.040535e+00 1.2535925000 1.783428750 ## b[2] -3.473550e-01 -0.2555277500 -0.069451788 ## b[3] -3.967245e-01 -0.2805037500 -0.087933813 ## b[4] -1.695455e-01 -0.0411909000 0.157096300 ## b[5] 1.476760e-01 0.2489355000 0.389850100 ## b[6] 5.613085e-01 0.6766462500 0.840970625 ## b[7] 3.991105e-01 0.4939210000 0.640443675 ## mus[1,1] 1.614485e+00 1.8156225000 2.070745250 ## mus[2,1] 1.423980e+00 1.5668150000 1.840773500 ## mus[3,1] 1.300640e+00 1.4518025000 1.727476750 ## mus[4,1] 1.318320e+00 1.4605025000 1.732440750 ## mus[5,1] 1.464910e+00 1.6142650000 1.823619500 ## mus[6,1] 1.659010e+00 1.7789150000 2.024115750 ## mus[7,1] 1.859670e+00 1.9703750000 2.170586500 ## mus[8,1] 2.156375e+00 2.2576325000 2.437298500 ## mus[9,1] 2.367605e+00 2.4732325000 2.685256000 ## mus[10,1] 2.272790e+00 2.3820250000 2.575945000 ## mus[11,1] 1.993480e+00 2.1138300000 2.320129750 ## mus[12,1] 1.689150e+00 1.7972125000 2.010837250 ## mus[13,1] 1.656005e+00 1.7621300000 1.971062500 ## mus[14,1] 1.382825e+00 1.5158225000 1.729462500 ## mus[15,1] 1.212015e+00 1.3455650000 1.571700500 ## mus[16,1] 1.139380e+00 1.2893950000 1.525885500 ## mus[17,1] 1.191470e+00 1.3394525000 1.558395000 ## mus[18,1] 1.295680e+00 1.4359175000 1.681703500 ## mus[19,1] 1.414405e+00 1.5538100000 1.785457000 ## mus[20,1] 1.642100e+00 1.7894575000 1.998301250 ## mus[21,1] 1.785415e+00 1.9358400000 2.188768250 ## mus[22,1] 1.649825e+00 1.8027650000 2.054714750 ## mus[23,1] 1.359240e+00 1.5120950000 1.743875000 ## mus[24,1] 1.032430e+00 1.1903250000 1.426930000 ## mus[25,1] 9.967740e-01 1.1506575000 1.393745500 ## mus[26,1] 7.533895e-01 0.9115580000 1.166935500 ## mus[27,1] 6.055615e-01 0.7614645000 1.038671500 ## mus[28,1] 5.887470e-01 0.7303415000 1.008063750 ## mus[29,1] 7.057955e-01 0.8443055000 1.114519750 ## mus[30,1] 8.752020e-01 1.0110650000 1.300109750 ## mus[31,1] 1.064260e+00 1.2014725000 1.460373000 ## mus[32,1] 1.345215e+00 1.4815900000 1.701511250 ## mus[33,1] 1.561190e+00 1.7086975000 1.942302250 ## mus[34,1] 1.485905e+00 1.6253875000 1.891557000 ## mus[35,1] 1.216095e+00 1.3820200000 1.636964250 ## mus[36,1] 9.140885e-01 1.0671700000 1.321080500 ## mus[37,1] 8.823385e-01 1.0456300000 1.311111500 ## mus[38,1] 6.223875e-01 0.7894405000 1.079071750 ## mus[39,1] 4.408895e-01 0.5968987500 0.938600925 ## mus[40,1] 3.480440e-01 0.5470192500 0.882869875 ## mus[41,1] 4.158045e-01 0.5766260000 0.906808400 ## mus[42,1] 5.103340e-01 0.6697732500 0.994978000 ## mus[43,1] 6.258185e-01 0.7828557500 1.064152000 ## mus[44,1] 8.714370e-01 1.0125125000 1.273441000 ## mus[45,1] 1.018680e+00 1.1790625000 1.453481750 ## mus[46,1] 8.768600e-01 1.0383550000 1.326553500 ## mus[47,1] 5.876210e-01 0.7301192500 1.002567400 ## mus[48,1] 2.643410e-01 0.4275630000 0.659043250 ## mus[49,1] 2.403865e-01 0.4065992500 0.630636575 ## mus[50,1] -1.717255e-02 0.1626157500 0.431334550 ## mus[51,1] -1.767890e-01 0.0154100250 0.321839875 ## mus[52,1] -1.768235e-01 0.0165229000 0.321865475 ## mus[53,1] -3.788290e-02 0.1357850000 0.476901125 ## mus[54,1] 1.443410e-01 0.2977095000 0.631415725 ## mus[55,1] 3.480610e-01 0.5084032500 0.795780525 ## mus[56,1] 6.580285e-01 0.8173577500 1.063439750 ## mus[57,1] 8.991965e-01 1.0711400000 1.351057750 ## mus[58,1] 8.605185e-01 1.0128575000 1.284001750 ## mus[59,1] 6.335585e-01 0.7658315000 1.056689750 ## mus[60,1] 3.790075e-01 0.5224172500 0.807550025 ## mus[61,1] 3.988670e-01 0.5506647500 0.819097850 ## mus[62,1] 2.026050e-01 0.3599412500 0.685124150 ## mus[63,1] 1.047265e-01 0.2656590000 0.627279800 ## mus[64,1] 1.048105e-01 0.3021547500 0.632590100 ## mus[65,1] 2.530680e-01 0.4459687500 0.748251375 ## mus[66,1] 4.649355e-01 0.6295537500 0.888877450 ## mus[67,1] 6.857355e-01 0.8341312500 1.105234250 ## mus[68,1] 1.006530e+00 1.1378775000 1.411462250 ## mus[69,1] 1.235265e+00 1.3896650000 1.647363500 ## mus[70,1] 1.184865e+00 1.3363250000 1.583974500 ## mus[71,1] 9.699405e-01 1.1297125000 1.411500750 ## mus[72,1] 7.182980e-01 0.8889820000 1.162595750 ## mus[73,1] 7.464990e-01 0.9316957500 1.236196250 ## mus[74,1] 5.585095e-01 0.7484497500 1.054687250 ## mus[75,1] 4.453250e-01 0.6584570000 1.017405750 ## rho[1] 3.653410e+00 3.9310050000 4.373320250 ## ypred[1,1] 5.000000e+00 7.0000000000 11.000000000 ## ypred[2,1] 4.000000e+00 5.0000000000 9.000000000 ## ypred[3,1] 4.000000e+00 5.0000000000 8.525000000 ## ypred[4,1] 4.000000e+00 5.0000000000 8.000000000 ## ypred[5,1] 4.000000e+00 6.0000000000 9.000000000 ## ypred[6,1] 5.000000e+00 7.0000000000 11.000000000 ## ypred[7,1] 6.000000e+00 8.0000000000 13.000000000 ## ypred[8,1] 8.000000e+00 10.0000000000 17.000000000 ## ypred[9,1] 1.000000e+01 13.0000000000 19.525000000 ## ypred[10,1] 9.000000e+00 12.0000000000 18.000000000 ## ypred[11,1] 7.000000e+00 9.0000000000 14.000000000 ## ypred[12,1] 5.000000e+00 7.0000000000 11.000000000 ## ypred[13,1] 5.000000e+00 7.0000000000 11.000000000 ## ypred[14,1] 4.000000e+00 6.0000000000 9.000000000 ## ypred[15,1] 3.000000e+00 4.2500000000 8.000000000 ## ypred[16,1] 3.000000e+00 4.0000000000 7.000000000 ## ypred[17,1] 3.000000e+00 5.0000000000 7.000000000 ## ypred[18,1] 4.000000e+00 5.0000000000 8.525000000 ## ypred[19,1] 4.000000e+00 5.0000000000 9.000000000 ## ypred[20,1] 5.000000e+00 7.0000000000 11.000000000 ## ypred[21,1] 6.000000e+00 8.0000000000 12.000000000 ## ypred[22,1] 5.000000e+00 7.0000000000 11.000000000 ## ypred[23,1] 4.000000e+00 5.0000000000 9.000000000 ## ypred[24,1] 3.000000e+00 4.0000000000 7.000000000 ## ypred[25,1] 2.000000e+00 4.0000000000 6.000000000 ## ypred[26,1] 2.000000e+00 3.0000000000 5.525000000 ## ypred[27,1] 1.000000e+00 2.0000000000 5.000000000 ## ypred[28,1] 1.000000e+00 3.0000000000 5.000000000 ## ypred[29,1] 2.000000e+00 3.0000000000 5.525000000 ## ypred[30,1] 2.000000e+00 3.0000000000 7.000000000 ## ypred[31,1] 3.000000e+00 4.0000000000 7.000000000 ## ypred[32,1] 4.000000e+00 5.0000000000 8.000000000 ## ypred[33,1] 5.000000e+00 6.0000000000 11.000000000 ## ypred[34,1] 4.000000e+00 6.0000000000 10.000000000 ## ypred[35,1] 3.000000e+00 5.0000000000 8.000000000 ## ypred[36,1] 2.000000e+00 3.0000000000 6.000000000 ## ypred[37,1] 2.000000e+00 3.0000000000 6.000000000 ## ypred[38,1] 2.000000e+00 3.0000000000 5.000000000 ## ypred[39,1] 1.000000e+00 2.0000000000 5.000000000 ## ypred[40,1] 1.000000e+00 2.0000000000 4.000000000 ## ypred[41,1] 1.000000e+00 2.0000000000 5.000000000 ## ypred[42,1] 1.000000e+00 2.0000000000 5.000000000 ## ypred[43,1] 2.000000e+00 3.0000000000 5.000000000 ## ypred[44,1] 2.000000e+00 3.0000000000 6.000000000 ## ypred[45,1] 3.000000e+00 4.0000000000 6.000000000 ## ypred[46,1] 2.000000e+00 4.0000000000 6.000000000 ## ypred[47,1] 2.000000e+00 3.0000000000 5.000000000 ## ypred[48,1] 1.000000e+00 2.0000000000 4.000000000 ## ypred[49,1] 1.000000e+00 2.0000000000 4.000000000 ## ypred[50,1] 1.000000e+00 2.0000000000 3.000000000 ## ypred[51,1] 1.000000e+00 1.0000000000 3.000000000 ## ypred[52,1] 1.000000e+00 1.0000000000 3.000000000 ## ypred[53,1] 1.000000e+00 2.0000000000 4.000000000 ## ypred[54,1] 1.000000e+00 2.0000000000 4.000000000 ## ypred[55,1] 1.000000e+00 2.0000000000 4.000000000 ## ypred[56,1] 2.000000e+00 3.0000000000 5.000000000 ## ypred[57,1] 2.000000e+00 4.0000000000 6.000000000 ## ypred[58,1] 2.000000e+00 4.0000000000 6.000000000 ## ypred[59,1] 2.000000e+00 3.0000000000 5.000000000 ## ypred[60,1] 1.000000e+00 2.0000000000 4.000000000 ## ypred[61,1] 1.000000e+00 2.0000000000 4.000000000 ## ypred[62,1] 1.000000e+00 2.0000000000 4.000000000 ## ypred[63,1] 1.000000e+00 2.0000000000 4.000000000 ## ypred[64,1] 1.000000e+00 2.0000000000 4.000000000 ## ypred[65,1] 1.000000e+00 2.0000000000 4.000000000 ## ypred[66,1] 1.000000e+00 2.0000000000 5.000000000 ## ypred[67,1] 2.000000e+00 3.0000000000 5.000000000 ## ypred[68,1] 3.000000e+00 4.0000000000 7.000000000 ## ypred[69,1] 3.000000e+00 5.0000000000 9.000000000 ## ypred[70,1] 3.000000e+00 4.0000000000 8.000000000 ## ypred[71,1] 2.000000e+00 4.0000000000 7.000000000 ## ypred[72,1] 2.000000e+00 3.0000000000 5.000000000 ## ypred[73,1] 2.000000e+00 3.0000000000 6.000000000 ## ypred[74,1] 2.000000e+00 3.0000000000 5.000000000 ## ypred[75,1] 1.000000e+00 2.0000000000 5.000000000 ## lp__ 6.809520e+01 71.1118250000 75.633600000 ``` ``` r model2$model_output@model_pars ``` ``` ## [1] "alpha_gp" "rho_gp" "b_gp" "lambda" "trend" "diag_SPD" ## [7] "SPD_beta" "b" "mus" "rho" "ypred" "lp__" ``` ``` r model2$model_output@sim$chains ``` ``` ## [1] 4 ``` ``` r model2$model_output@sim$iter ``` ``` ## [1] 1000 ``` --- ## Draws of `trend` .panelset[ .panel[.panel-name[Code] ``` r # view posterior draws of the trend plot(model2, type = 'trend', realisations = TRUE, n_realisations = 10) ``` ] .panel[.panel-name[Plot] .center[] ] ] --- class: middle center ### But how can we extrapolate these to the future? <br> ### Ready for some multivariate statistical .multicolor[wizardry]? --- class: black-inverse .center[.grey[.big[Ready]]] <img src="resources/momoa.gif" style="position:fixed; right:30%; top:25%; width:480px; height:381px; border:none;"/> --- ## <svg aria-hidden="true" role="img" viewBox="0 0 576 512" style="height:1em;width:1.12em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M234.7 42.7L197 56.8c-3 1.1-5 4-5 7.2s2 6.1 5 7.2l37.7 14.1L248.8 123c1.1 3 4 5 7.2 5s6.1-2 7.2-5l14.1-37.7L315 71.2c3-1.1 5-4 5-7.2s-2-6.1-5-7.2L277.3 42.7 263.2 5c-1.1-3-4-5-7.2-5s-6.1 2-7.2 5L234.7 42.7zM46.1 395.4c-18.7 18.7-18.7 49.1 0 67.9l34.6 34.6c18.7 18.7 49.1 18.7 67.9 0L529.9 116.5c18.7-18.7 18.7-49.1 0-67.9L495.3 14.1c-18.7-18.7-49.1-18.7-67.9 0L46.1 395.4zM484.6 82.6l-105 105-23.3-23.3 105-105 23.3 23.3zM7.5 117.2C3 118.9 0 123.2 0 128s3 9.1 7.5 10.8L64 160l21.2 56.5c1.7 4.5 6 7.5 10.8 7.5s9.1-3 10.8-7.5L128 160l56.5-21.2c4.5-1.7 7.5-6 7.5-10.8s-3-9.1-7.5-10.8L128 96 106.8 39.5C105.1 35 100.8 32 96 32s-9.1 3-10.8 7.5L64 96 7.5 117.2zm352 256c-4.5 1.7-7.5 6-7.5 10.8s3 9.1 7.5 10.8L416 416l21.2 56.5c1.7 4.5 6 7.5 10.8 7.5s9.1-3 10.8-7.5L480 416l56.5-21.2c4.5-1.7 7.5-6 7.5-10.8s-3-9.1-7.5-10.8L480 352l-21.2-56.5c-1.7-4.5-6-7.5-10.8-7.5s-9.1 3-10.8 7.5L416 352l-56.5 21.2z"/></svg> ``` r sim_gp = function(trend_draw, h, rho, alpha){ # extract training and testing times t <- 1:length(trend_draw); t_new <- 1:(length(trend_draw) + h) # calculate training covariance Sigma <- alpha ^ 2 * exp(-0.5 * ((outer(t, t, "-") / rho) ^ 2)) + diag(1e-9, length(t)) # calculate training vs testing cross-covariance Sigma_new <- alpha ^ 2 * exp(-0.5 * ((outer(t, t_new, "-") / rho) ^ 2)) # calculate testing covariance Sigma_star <- alpha ^ 2 * exp(-0.5 * ((outer(t_new, t_new, "-") / rho) ^ 2)) + diag(1e-9, length(t_new)) # draw one function realization of the stochastic Gaussian Process t(Sigma_new) %*% solve(Sigma, trend_draw) + MASS::mvrnorm(1, mu = rep(0, length(t_new)), Sigma = Sigma_star - t(Sigma_new) %*% solve(Sigma, Sigma_new)) } ``` --- ## .multicolor[Wizardize] one trend draw .panelset[ .panel[.panel-name[Wizardry] ``` r # extract trend parameter draws and plot one draw trend_draws <- as.matrix(model2, variable = 'trend', regex = TRUE) alpha_draws <- as.matrix(model2, variable = 'alpha_gp', regex = TRUE) rho_draws <- as.matrix(model2, variable = 'rho_gp', regex = TRUE) plot(1, type = 'n', bty = 'l', xlim = c(1, 130), ylim = range(trend_draws[1,]), ylab = 'One trend draw', xlab = 'Time') lines(trend_draws[1,], col = 'gray70', lwd = 3.5) # wizardize to extend draw forward 30 timesteps and plot forecast_draw = sim_gp(trend_draw = trend_draws[1,], h = 30 alpha = alpha_draws[1,], rho = rho_draws[1,]) lines(x = 101:130, y = forecast_draw[101:130], lwd = 3.5, col = 'darkred') abline(v = 100.5, lty = 'dashed', lwd = 2.5) ``` ] .panel[.panel-name[Plot] .center[] ] ] --- class: black-inverse .center[.grey[.big[Piece of cake?]]] <img src="resources/confused.gif" style="position:fixed; right:10%; top:20%; width:960px; height:518px; border:none;"/> --- class: middle center ### There is no wizardry <svg aria-hidden="true" role="img" viewBox="0 0 512 512" style="height:1em;width:1em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M175.9 448c-35-.1-65.5-22.6-76-54.6C67.6 356.8 48 308.7 48 256C48 141.1 141.1 48 256 48s208 93.1 208 208s-93.1 208-208 208c-28.4 0-55.5-5.7-80.1-16zM0 256a256 256 0 1 0 512 0A256 256 0 1 0 0 256zM128 369c0 26 21.5 47 48 47s48-21 48-47c0-20-28.4-60.4-41.6-77.7c-3.2-4.4-9.6-4.4-12.8 0C156.6 308.6 128 349 128 369zm128-65c-13.3 0-24 10.7-24 24s10.7 24 24 24c30.7 0 58.7 11.5 80 30.6c9.9 8.8 25 8 33.9-1.9s8-25-1.9-33.9C338.3 320.2 299 304 256 304zm47.6-96a32 32 0 1 0 64 0 32 32 0 1 0 -64 0zm-128 32a32 32 0 1 0 0-64 32 32 0 1 0 0 64z"/></svg>. Rather, each kind of trend (AR, GP etc...) has an underlying stochastic equation that can be used to extrapolate draws to the future <br> ### But doing this manually is slow and error-prone. `mvgam` does this *automatically* using `newdata` --- `plot(model2, type = 'trend', n_realisations = 4)` <img src="lecture_4_slidedeck_files/figure-html/unnamed-chunk-16-1.png" style="display: block; margin: auto;" /> --- `plot(model2, type = 'trend', n_realisations = 8)` <img src="lecture_4_slidedeck_files/figure-html/unnamed-chunk-17-1.png" style="display: block; margin: auto;" /> --- `plot(model2, type = 'trend', n_realisations = 30)` <img src="lecture_4_slidedeck_files/figure-html/unnamed-chunk-18-1.png" style="display: block; margin: auto;" /> --- `plot(model2, type = 'trend', n_realisations = 60)` <img src="lecture_4_slidedeck_files/figure-html/unnamed-chunk-19-1.png" style="display: block; margin: auto;" /> --- `plot(model2, type = 'trend')` <img src="lecture_4_slidedeck_files/figure-html/unnamed-chunk-20-1.png" style="display: block; margin: auto;" /> --- class: middle center ### Once dynamic trend is extrapolated, computing forecasts is easy <br> ### We only need to supply any remaining "future" predictor values from covariates --- class: middle center ### Covariate predictions are added to the trend predictions to give the full predictions *on the link scale* <br> ### `mvgam` does this *automatically* using the `forecast()` function --- `plot(forecast(model2, type = 'link'), realisations = TRUE)` <img src="lecture_4_slidedeck_files/figure-html/unnamed-chunk-21-1.png" style="display: block; margin: auto;" /> --- class: inverse middle center big-subsection # Live code example --- class: middle center ### Forecasting is easier if `newdata` passed to `mvgam()`, but this results in a larger model object and requires test data be available now <br> ### When testing data not available, you can generate forecasts for new data later using `forecast()` (note, `time` values in `newdata` must follow immediately from `time` values in original training data) <br> ### But there are multiple *types* of predictions available. What are they? --- background-image: url('./resources/response_types.svg') background-size: contain ## Types of `mvgam` predictions <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> .small[modified from [Heiss 2022](https://www.andrewheiss.com/blog/2022/09/26/guide-visualizing-types-posteriors/)] --- ## `mvgam` and `brms` 📦's <br> | Type | `mvgam` | `brms` | |--------------------|----------------|------------------------------| | link | `predict(type = 'link')` | `posterior_linpred()` | | expected | `predict(type = 'expected')` | `posterior_epred()` | | response | `predict(type = 'response')` | `posterior_predict()` | For all `mvgam` predictions, whether to include error in the dynamic process can be controlled using `process_error = TRUE` or `process_error = FALSE` --- class: middle center ### How should *you* use these predictions? <br> ### 1. Don't interpret coefficients. Rather, use predictions on both the link and expectation scale to understand the model better <br> ### 2. Compare predictions on the response scale to the observed data using posterior predictive checks and `loo()` to diagnose problems <br> ### 3. Make out-of-sample predictions and evaluate with proper scoring rules --- ## Don't interpret coefficients ``` r coef(model) ``` ``` ## 2.5% 50% 97.5% Rhat n_eff ## (Intercept) 0.4244452 0.9973625 1.87272150 1.01 377 ## s(season).1 -0.6285627 -0.3477210 -0.06202533 1.00 1661 ## s(season).2 -0.7338488 -0.3920205 -0.05727605 1.00 1993 ## s(season).3 -0.4865379 -0.1625075 0.13829287 1.00 2374 ## s(season).4 -0.1564071 0.1396100 0.42328822 1.00 2229 ## s(season).5 0.2798351 0.5486395 0.82546612 1.00 2148 ## s(season).6 0.1263498 0.3864325 0.63401010 1.00 2116 ``` --- ## Don't interpret coefficients These coefficients are acting on the .emphasize[*link scale*] - Often result in nonlinear relationships on response scale - Very often, the coefficients are .emphasize[*correlated somehow*] - This is especially the case in GAMs! - Don't worry about *p*-values or intervals, use .emphasize[*posterior predictions*] instead Start with .emphasize[*partial effects*] on link scale - These are conditional on all other effects being zero - negative values &#8680; covariate reduces the response - positive values &#8680; covariate increases the response --- `draw(model)` <img src="lecture_4_slidedeck_files/figure-html/unnamed-chunk-23-1.png" style="display: block; margin: auto;" /> --- ## `link` predictions `predict(object, type = 'link')` Gives the real-valued, unconstrained linear predictor - Takes into account uncertainty in GAM regression coefficients - Can include uncertainty in any dynamic trend components --- ## `link` predictions .panelset[ .panel[.panel-name[Code] ``` r # extract link-scale forecasts from the model fc <- forecast(model, type = 'link') # plot using the available S3 plotting function plot(fc) ``` ] .panel[.panel-name[Plot] .center[] ] ] --- class: middle center ### Ok. but what do these things actually, really *mean*? --- class: black-inverse <img src="resources/marginaleffects_need.jpg" style="position:fixed; right:40%; top:1%; width:233px; height:658px; border:none;"/> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> .small[[Credit @stephenjwild](https://twitter.com/stephenjwild/status/1687499914794643456?s=20)] --- ## `expected` predictions `predict(object, type = 'expected')` Gives the .emphasize[*average*] prediction on the observation (response) scale - Useful as we often want to get a sense of long-term averages for guiding scenario analyses - .emphasize[*Usually*] it is just the inverse link function applied to a prediction from `type = link` This is the most confusing type of prediction, as using `predict(model, type = 'response')` for models fitted in `gam()` or `glm()` actually return .emphasize[*expectations*] --- ## `expected` predictions .panelset[ .panel[.panel-name[Code] ``` r # extract expectation-scale forecasts from the model fc <- forecast(model, type = 'expected') # plot using the available S3 plotting function plot(fc) ``` ] .panel[.panel-name[Plot] .center[] ] ] --- ## `response` predictions `predict(object, type = 'response')` Gives the predictions on the observation (response) scale - Includes uncertainty in the linear predictor .emphasize[*and*] any uncertainty arising from the observation process - Some distributions only depend on the inverse link of the linear predictor (i.e. `\(Poisson(\lambda)\)` or `\(Bernoulli(\pi)\)`)) - Others depend on additional shape / scale parameters (i.e. `\(Normal(\mu,\sigma)\)` or `\(StudentT(\nu,\mu,\sigma)\)`) These are the most often used for evaluating forecasts --- ## Interpreting on the *response* scale Some key questions you should ask of a fitted model - Can the model simulate realistic data? - Does the model capture salient features of the data that you'd like to predict? - What criteria would you use to determine whether one model is more suitable than another? Very often, these questions can only be answered by looking at what kinds of predictions a model makes .emphasize[*on the response scale*] --- ## `response` predictions .panelset[ .panel[.panel-name[Code] ``` r # extract response-scale forecasts from the model fc <- forecast(model, type = 'response') # plot using the available S3 plotting function plot(fc) ``` ] .panel[.panel-name[Plot] .center[] ] ] --- class: inverse middle center big-subsection # Posterior predictive checks --- ## Posterior predictive checks Statistical models can be used to generate (i.e. simulate) new outcome data - Can either use the same covariates used to train the model - Or can use `newdata` for scenario modelling (including forecasting) To generate new outcome data we can simulate from the model's posterior predictive distribution "*The idea is simple: if a model is a good fit then we should be able to use it to generate data that looks a lot like the data we observed*" [Gabry & Mahr](https://mc-stan.org/bayesplot/reference/PPC-overview.html) --- ## A PPC barplot .panelset[ .panel[.panel-name[Code] ``` r # view barplots of true data vs simulated predictions pp_check(model, type = 'bars', ndraws = 25) ``` ] .panel[.panel-name[Plot] .center[] ] ] --- ## A PPC cumulative distribution .panelset[ .panel[.panel-name[Code] ``` r # view the simulated vs true cumulative distribution functions pp_check(model, type = 'ecdf_overlay', ndraws = 25) ``` ] .panel[.panel-name[Plot] .center[] ] ] --- ## A PIT CDF .panelset[ .panel[.panel-name[Code] ``` r # view the simulated vs true count frequencies pp_check(model, type = 'pit_ecdf') ``` ] .panel[.panel-name[Plot] .center[] ] ] --- ## Comparing fits with `loo()` ``` r model_good <- mvgam( y ~ s(season, bs = 'cc', k = 8) + * gp(time, k = 20, c = 5/4, scale = FALSE), data = data_train, trend_model = 'None', family = poisson() ) ``` A GP of `time`, together with the cyclic seasonality, is a good model here --- ## Comparing fits with `loo()` ``` r model_bad <- mvgam( y ~ 1, data = data_train, * trend_model = RW(), family = poisson() ) ``` A RW with no seasonality will fit the data *very well*, but will not *generalize* well --- `plot(hindcast(model_good))` <img src="lecture_4_slidedeck_files/figure-html/unnamed-chunk-32-1.png" style="display: block; margin: auto;" /> --- `plot(hindcast(model_bad))` <img src="lecture_4_slidedeck_files/figure-html/unnamed-chunk-33-1.png" style="display: block; margin: auto;" /> --- `plot_predictions(model_good, by = 'time')` <img src="lecture_4_slidedeck_files/figure-html/unnamed-chunk-34-1.png" style="display: block; margin: auto;" /> --- `plot_predictions(model_bad, by = 'time')` <img src="lecture_4_slidedeck_files/figure-html/unnamed-chunk-35-1.png" style="display: block; margin: auto;" /> --- ## Comparing fits with `loo()` `loo_compare(model_good, model_bad)` ``` ## elpd_diff se_diff ## model_good 0.0 0.0 ## model_bad -300.4 33.8 ``` A much lower Expected Log Predictive Density (ELPD) for `model_bad` suggests that this model would not do as well when tasked with predicting against a *new* set of observations --- class: middle center ### PPCs and `loo()` using training covariates are a great first step to check model validity and begin comparing models <br> ### But they only assess how well the model predicts against the training data <br> ### How else can we verify models? Using `newdata` for response predictions &#8680; counterfactual .emphasize[*scenarios*] --- class: inverse middle center big-subsection # Prediction-based inferences --- ## Marginal & conditional predictions "*Applied researchers are keen to report simple quantities that carry clear scientific meaning*" ([Arel-Bundock 2023](https://marginaleffects.com/)) This is often challenging because: - Intuitive estimands and uncertainties are tedious to compute - Nonlinear terms, nonlinear link functions, interaction effects and observation parameters all make these effects nearly impossible to access from coefficients alone - Most software emphasizes coefficients and *p*-values over meaningful interpretations --- ## `predict.mvgam()` Pass `newdata` consisting of particular covariate values that represent scenarios you'd like to explore - Can be simple: predict a smooth function along a fine-spaced grid to explore the smooth's shape and / or derivatives - Or can be complex: integrate over a high-dimensional grid of predictors to understand the average impact of a predictor on the response Users can implement the wonderful `datagrid()` function from `marginaleffects` 📦 to effortlessly generate a `data.frame` of covariate values for scenario predictions --- ## Conditional smooths .panelset[ .panel[.panel-name[Code] ``` r # use plot_predictions() to visualise conditional effects # on the scale of the response plot_predictions(model, condition = 'season', points = 0.5, process_error = FALSE) ``` ] .panel[.panel-name[Plot] .center[] ] ] --- ## Rates of change .panelset[ .panel[.panel-name[Code] ``` r # use plot_slopes() to visualise rates of change # on the expectation scale of the response plot_slopes(model, variables = 'season', by = 'season', type = 'expected', process_error = FALSE) + geom_hline(yintercept = 0, linetype = 'dashed') ``` ] .panel[.panel-name[Plot] .center[] ] ] --- ## Finding peak growth ``` r # estimate when the `season` smooth grows at its fastest rate max_growth = function(hi, lo, x) { dydx <- (hi - lo) / 1e-6; x[dydx == max(dydx)][1] } comparisons( model, type = 'link', newdata = datagrid(season = seq(0, 12, length.out = 200)), variables = list("season" = 1e-6), comparison = max_growth ) ``` ``` ## ## Estimate 2.5 % 97.5 % ## 7.6 4.34 8.26 ## ## Term: season ## Type: link ## Comparison: +1e-06 ``` --- ## Posterior contrasts .panelset[ .panel[.panel-name[Code] ``` r # take draws of average comparison between season = 9 vs season = 3 avg_comparisons( model, variables = list(season = c(9, 3)), process_error = FALSE ) %>% posterior_draws() %>% # use the resulting posterior draw object to plot a density of the # posterior contrasts ggplot(aes(x = draw)) + # use the stat_halfeye function from tidybayes for a nice visual stat_halfeye(fill = "#C79999") + labs(x = "(season = 9) − (season = 3)", y = "Density", title = "Average posterior contrast") ``` ] .panel[.panel-name[Plot] .center[] ] ] --- class: middle center ### The ability to readily interpret models from `mvgam` and `brms` 📦's is a .emphasize[*huge advantage*] over traditional time series models. See [my blogpost on interpeting GAMs for more examples](https://ecogambler.netlify.app/blog/interpreting-gams/) <br> ### But this is a forecasting course. So how can we evaluate forecast distributions? --- ## The forecasting workflow "*The accuracy of forecasts can only be determined by considering how well a model performs on new data that were not used when fitting the model.*" [Hyndman and Athanasopoulos](https://otexts.com/fpp3/accuracy.html) We must evaluate on data that was not used to train the model (i.e. .emphasize[*leave-future-out cross-validation*]) because: - Models that fit training data well do not always provide good forecasts - We can easily engineer a model that perfectly fits the training data, leading to overfitting - See [the `mvgam` forecasting vignette](https://nicholasjclark.github.io/mvgam/articles/forecast_evaluation.html) for more guidance --- ## Leave-future-out CV Important to train the model on some portion of data and use a hold-out portion (test data) to evaluate forecasts: `$$p(y_{T+H}|y_{1:T})$$` Some points to consider: - The test set should ideally be at least as large as the maximum forecast horizon required for decision-making - Ideally, this process would be repeated many times to incorporate variation in forecast performance - Usually good to compare models against simpler .emphasize[*benchmark*] models to ensure added complexity improves forecasts --- class: middle center ### We must obtain leave-future-out forecasts (ideally for many different training / testing splits) to compare ecological forecasting models <br> ### But how do we *evaluate* forecasts? <br> ### The most common evaluation practice in forecasting tasks is to evaluate point predictions --- class: inverse middle center big-subsection # Point-based forecast evaluation --- ## Forecast errors A forecast error (or forecast residual) is the difference between the true value in an out-of-sample set and the predicted response value: `$$\epsilon_{T+H}=\boldsymbol{y}_{T+H} - \hat{y}_{T+H}$$` Where: - `\(T\)` is the total length of the training set - `\(H\)` is the forecast horizon - `\(\hat{y}_{T+H}\)` is the prediction at time `\(T+H\)` Point-based measures use these errors in different ways --- ## Common point-based measures Scale-dependent measures - Mean Absolute Error: `\(mean(|\epsilon_t|)\)` - Root Mean Squared Error: `\(\sqrt{mean(\epsilon_t^2)}\)` Scale-independent measures - Mean Absolute Percentage Error: `\(mean(|p_t|)\)`, where `\(p_t=100\epsilon_t/y_t\)` - Mean Absolute Scaled Error: `\(mean(|q_t|)\)`, where `\(q_t\)` is the error scaled against errors from an appropriate .emphasize[*benchmark*] forecast Lower values are better for all these measures --- class: middle center ### We won't dwell much on point-based measures because ecological predictions and their associated management decisions are inherently *uncertain* ([but see this video for more details](https://www.youtube.com/watch?v=ek5xLEoQN3E&t=5s)) <br> ### Point-based measures ignore far too much information in the forecast distribution <br> ### It is better to evaluate the *entire forecast distribution* --- class: inverse middle center big-subsection # Probabilistic forecast evaluation --- ## Scaled Interval Score A common step to evaluate a forecast distribution is to [compute how well it's prediction intervals perform](https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1008618): `$$SIS = (U_{t} - L_{t}) + \frac{2}{\alpha}(L_{t} - y_{t})\mathcal{1}(y_{t} < L_{t}) + \frac{2}{\alpha}(y_{t} - U_{t})\mathcal{1}(y_{t} > U_{t})$$` Where: - `\(y_{t}\)` is the true observed value at horizon `\(H\)` - `\(\alpha\)` is `\(1-\text{interval width}\)` - The `\(100(1−\alpha)\%\)` interval for horizon `\(H\)` is `\([L_{t}, U_{t}|\)` - `\(1\)` is a binary indicator function --- ## Penalize *overly precise* forecasts <img src="lecture_4_slidedeck_files/figure-html/unnamed-chunk-41-1.png" style="display: block; margin: auto;" /> --- ## Evaluating the full distribution Interval scores are very useful when we want to target a particular interval or if we don't have the full distribution - Allows different teams to submit a few intervals rather than thousands of posterior samples - Can compare forecasts from many different algorithms / models But if we do have a full distribution, we have other options "*Scoring rules provide summary measures for the evaluation of probabilistic forecasts, by assigning a numerical score based on the predictive distribution and on the event or value that materializes*" ([Gneiting and Raftery 2007](https://sites.stat.washington.edu/raftery/Research/PDF/Gneiting2007jasa.pdf)) --- ## What is a good forecast? Reliable: good probabilistic calibration Sharp: informative, with tight enough intervals to guide decisions Skilled: performs better overall than simpler benchmark forecasts Proper scoring rules attempt to address each of these goals using the full forecast distribution --- background-image: url('./resources/dnorm.svg') ## Predictive density --- ## Log predictive density Compute *log(probability)* of a given truth given distributional assumptions: `$$log~p(y_{T+H}|y_{t:T},\theta)$$` Use density functions in <svg aria-hidden="true" role="img" viewBox="0 0 581 512" style="height:1em;width:1.13em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:steelblue;overflow:visible;position:relative;"><path d="M581 226.6C581 119.1 450.9 32 290.5 32S0 119.1 0 226.6C0 322.4 103.3 402 239.4 418.1V480h99.1v-61.5c24.3-2.7 47.6-7.4 69.4-13.9L448 480h112l-67.4-113.7c54.5-35.4 88.4-84.9 88.4-139.7zm-466.8 14.5c0-73.5 98.9-133 220.8-133s211.9 40.7 211.9 133c0 50.1-26.5 85-70.3 106.4-2.4-1.6-4.7-2.9-6.4-3.7-10.2-5.2-27.8-10.5-27.8-10.5s86.6-6.4 86.6-92.7-90.6-87.9-90.6-87.9h-199V361c-74.1-21.5-125.2-67.1-125.2-119.9zm225.1 38.3v-55.6c57.8 0 87.8-6.8 87.8 27.3 0 36.5-38.2 28.3-87.8 28.3zm-.9 72.5H365c10.8 0 18.9 11.7 24 19.2-16.1 1.9-33 2.8-50.6 2.9v-22.1z"/></svg>, such as `dnorm` or `dnbinom`; higher values are better `\(\theta\)` captures all unknown parameters: - Regression coefficients `\(\beta\)` - Dynamic parameters; `\(\alpha\)` or `\(\rho\)` for GP; `\(\sigma_{error}\)` for RW - Observation parameters; `\(\nu\)` for StudentT or `\(\sigma_{obs}\)` for Normal --- class: middle center ### logging is stabile and makes joint calculations easier <br> ### But the log score can severly penalize over-confidence and is sensitive to outliers <br> ### Other proper scoring rules can provide more robust comparisons, without needing to rely on distributional assumptions --- ## CRPS Continuous Ranked Probability Score compares true Cumulative Distribution Function (CDF) to forecast CDF $$ CRPS(F,y)=\int_{-\infty}^{\infty}(F(\hat{y}) - \mathcal{1}(\hat{y}\geq y))^2dy$$ Where: - `\(F(\hat{y})\)` is the forecast CDF evaluated at many points - `\(\mathcal{1}(\hat{y}\geq y)\)` gives the true observed CDF SIS converges to CRPS when evaluating an increasing number of equally spaced intervals --- ## CRPS <img src="lecture_4_slidedeck_files/figure-html/unnamed-chunk-42-1.png" style="display: block; margin: auto;" /> --- class: middle center ### CRPS useful for both parametric and non-parametric predictions because we just need to calculate the CDF of the forecast distribution <br> ### Penalises over- and under-confidence similarly, and gives more stable handling of outliers <br> ### Score is on the scale of the outcome variable being forecasted, so is somewhat intuitive (a lower score is better) --- ## DRPS Similar to CRPS, the discrete version (DRPS) can be used to evaluate a forecast that is composed only of integers Uses an approximation of the forecast and true CDFs at a range of possible count values Interpretation is similar --- ## `score.mvgam_forecast()` Once forecasts are computed and stored in an object of class `mvgam_forecast`, scores can be directly applied User chooses among the Scaled Interval Score (`sis`), log score (`elpd`), CRPS (`crps`), DRPS (`drps`) and two multivariate scores (`energy` or `variogram`; more on this in the next lecture) User also specifies an interval for calculating coverage and/or which interval to use for the Scaled Interval Score `return` is a `list()` with scores for each series in the data and an overall score (usually just the sum of series-level scores) --- ``` r sc <- score(forecast(model), * score = 'crps', interval = 0.90) sc$series_1[1:10,] ``` ``` ## score in_interval interval_width eval_horizon score_type ## 1 0.9475925 1 0.9 1 crps ## 2 4.2706693 0 0.9 2 crps ## 3 1.9558260 1 0.9 3 crps ## 4 4.0117590 0 0.9 4 crps ## 5 1.6035490 1 0.9 5 crps ## 6 6.3143580 0 0.9 6 crps ## 7 0.6937460 1 0.9 7 crps ## 8 3.9872183 1 0.9 8 crps ## 9 1.4215897 1 0.9 9 crps ## 10 0.8361572 1 0.9 10 crps ``` Calculating the CRPS using the previously generated forecasts --- ``` r sc <- score(forecast(model), * score = 'sis', interval = 0.90) sc$series_1[1:10,] ``` ``` ## score in_interval interval_width eval_horizon score_type ## 1 4 1 0.9 1 sis ## 2 45 0 0.9 2 sis ## 3 6 1 0.9 3 sis ## 4 27 0 0.9 4 sis ## 5 8 1 0.9 5 sis ## 6 50 0 0.9 6 sis ## 7 10 1 0.9 7 sis ## 8 9 1 0.9 8 sis ## 9 8 1 0.9 9 sis ## 10 8 1 0.9 10 sis ``` Calculating the SIS using the previously generated forecasts; values outside interval are more heavily penalized --- ## How does `model_good` perform? .panelset[ .panel[.panel-name[Code] ``` r fc_good <- forecast( model_good, newdata = data_test ) plot(fc_good) ``` ] .panel[.panel-name[Plot] .center[] ] ] --- ## How does `model_bad` perform? .panelset[ .panel[.panel-name[Code] ``` r fc_bad <- forecast( model_bad, newdata = data_test ) plot(fc_bad) ``` ] .panel[.panel-name[Plot] .center[] ] ] --- ## How would an *ensemble* perform? .panelset[ .panel[.panel-name[Code] ``` r ens <- ensemble( fc_good, fc_bad ) plot(ens) ``` ] .panel[.panel-name[Plot] .center[] ] ] --- class: middle center ### We have seen how to produce out-of-sample forecasts from `mvgam` models and evaluate them against new observations <br> ### We have also investigated other ways that models can be critiqued, particularly making use of conditional predictions using `newdata` <br> ### But so far we have only considered univariate investigations. What happens if we want to forecast *multiple time series*? --- ## In the next lecture, we will cover Multivariate ecological time series Vector autoregressive processes Dynamic factor models Multivariate forecast evaluation