Draws from the Expected Value of the Posterior Predictive Distribution

Compute posterior draws of the expected value of the posterior predictive distribution (i.e. the conditional expectation). Can be performed for the data used to fit the model (posterior predictive checks) or for new data. By definition, these predictions have smaller variance than the posterior predictions performed by the posterior_predict.mvgam method. This is because only the uncertainty in the expected value of the posterior predictive distribution is incorporated in the draws computed by posterior_epred while the residual error is ignored there. However, the estimated means of both methods averaged across draws should be very similar.

Usage

# S3 method for mvgam
posterior_epred(
  object,
  newdata,
  data_test,
  ndraws = NULL,
  process_error = TRUE,
  ...
)

Arguments

object: list object returned from mvgam. See mvgam()
newdata: Optional dataframe or list of test data containing the same variables that were included in the original data used to fit the model. If not supplied, predictions are generated for the original observations used for the model fit.
data_test: Deprecated. Still works in place of newdata but users are recommended to use newdata instead for more seamless integration into R workflows
ndraws: Positive integer indicating how many posterior draws should be used. If NULL (the default) all draws are used.
process_error: Logical. If TRUE and newdata is supplied, expected uncertainty in the process model is accounted for by using draws from any latent trend SD parameters. If FALSE, uncertainty in the latent trend component is ignored when calculating predictions. If no newdata is supplied, draws from the fitted model's posterior predictive distribution will be used (which will always include uncertainty in any latent trend components)
...: Ignored

Value

A matrix of dimension n_samples x new_obs, where n_samples is the number of posterior samples from the fitted object and n_obs is the number of observations in newdata

Details

Note that for all types of predictions for models that did not include a trend_formula, uncertainty in the dynamic trend component can be ignored by setting process_error = FALSE. However, if a trend_formula was supplied in the model, predictions for this component cannot be ignored. If process_error = TRUE, trend predictions will ignore autocorrelation coefficients or GP length scale coefficients, ultimately assuming the process is stationary. This method is similar to the types of posterior predictions returned from brms models when using autocorrelated error predictions for newdata. This function is therefore more suited to posterior simulation from the GAM components of a mvgam model, while the forecasting functions plot_mvgam_fc and forecast.mvgam are better suited to generate h-step ahead forecasts that respect the temporal dynamics of estimated latent trends.

Examples

# \donttest{
# Simulate some data and fit a model
simdat <- sim_mvgam(n_series = 1, trend_model = 'AR1')
mod <- mvgam(y ~ s(season, bs = 'cc'),
            trend_model = AR(),
            noncentred = TRUE,
            data = simdat$data_train)
#> Compiling Stan program using cmdstanr
#> 
#> In file included from stan/lib/stan_math/stan/math/prim/prob/von_mises_lccdf.hpp:5,
#>                  from stan/lib/stan_math/stan/math/prim/prob/von_mises_ccdf_log.hpp:4,
#>                  from stan/lib/stan_math/stan/math/prim/prob.hpp:359,
#>                  from stan/lib/stan_math/stan/math/prim.hpp:16,
#>                  from stan/lib/stan_math/stan/math/rev.hpp:16,
#>                  from stan/lib/stan_math/stan/math.hpp:19,
#>                  from stan/src/stan/model/model_header.hpp:4,
#>                  from C:/Users/uqnclar2/AppData/Local/Temp/RtmpARA4r4/model-1333cfce30f1.hpp:2:
#> stan/lib/stan_math/stan/math/prim/prob/von_mises_cdf.hpp: In function 'stan::return_type_t<T_x, T_sigma, T_l> stan::math::von_mises_cdf(const T_x&, const T_mu&, const T_k&)':
#> stan/lib/stan_math/stan/math/prim/prob/von_mises_cdf.hpp:194: note: '-Wmisleading-indentation' is disabled from this point onwards, since column-tracking was disabled due to the size of the code/headers
#>   194 |       if (cdf_n < 0.0)
#>       | 
#> stan/lib/stan_math/stan/math/prim/prob/von_mises_cdf.hpp:194: note: adding '-flarge-source-files' will allow for more column-tracking support, at the expense of compilation time and memory
#> Start sampling
#> Running MCMC with 4 parallel chains...
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# Compute posterior expectations
expectations <- posterior_epred(mod)
str(expectations)
#>  num [1:2000, 1:75] 0.824 0.477 0.46 0.956 0.337 ...
# }