Time series modeling with Bayesian Dynamic Generalized Additive Models

.title[
# Time series modeling with Bayesian Dynamic Generalized Additive Models
]
.author[
### Nicholas Clark
]
.institute[
### School of Veterinary Science, University of Queensland, Australia
]
.date[
### Wednesday 13th December, 2023
]

---

---
class: animated fadeIn
background-image: url('./resources/smooth_only.gif')
## GAMs use splines `$(f(x))$` ...

---

background-image: url('./resources/basis_weights.gif')
## ...made of weighted basis functions

---

background-image: url('./resources/smooth_to_data.gif')
## Penalize `$f"(x)$` to learn weights

---

## Easy to fit 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>
<img align="center" width="306" height="464" src="resources/gam_book.jpg" style="float: right; 
  margin: 10px;">
`$$\mathbb{E}(\boldsymbol{Y_t}|\boldsymbol{X_t})=g^{-1}(\alpha + \sum_{j=1}^{J}f(x_{jt}))$$`

<br/>
Where: 
- `$g^{-1}$` is the inverse of the link function
- `${\alpha}$` is the intercept
- `$f(x)$` are potentially nonlinear functions of the `$J$` predictors

---

---

## What's the catch?

---

## A spline of `time`

```r
library(mgcv)
*model <- gam(y ~ s(time, k = 20, bs = 'bs', m = 2),
                data = data,
                family = gaussian())
```

A B-spline (`bs = 'bs'`) with `m = 2` sets the penalty on the second derivative

---

## Hindcasts <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="M464 256A208 208 0 1 0 48 256a208 208 0 1 0 416 0zM0 256a256 256 0 1 1 512 0A256 256 0 1 1 0 256zm177.6 62.1C192.8 334.5 218.8 352 256 352s63.2-17.5 78.4-33.9c9-9.7 24.2-10.4 33.9-1.4s10.4 24.2 1.4 33.9c-22 23.8-60 49.4-113.6 49.4s-91.7-25.5-113.6-49.4c-9-9.7-8.4-24.9 1.4-33.9s24.9-8.4 33.9 1.4zm40-89.3l0 0 0 0-.2-.2c-.2-.2-.4-.5-.7-.9c-.6-.8-1.6-2-2.8-3.4c-2.5-2.8-6-6.6-10.2-10.3c-8.8-7.8-18.8-14-27.7-14s-18.9 6.2-27.7 14c-4.2 3.7-7.7 7.5-10.2 10.3c-1.2 1.4-2.2 2.6-2.8 3.4c-.3 .4-.6 .7-.7 .9l-.2 .2 0 0 0 0 0 0c-2.1 2.8-5.7 3.9-8.9 2.8s-5.5-4.1-5.5-7.6c0-17.9 6.7-35.6 16.6-48.8c9.8-13 23.9-23.2 39.4-23.2s29.6 10.2 39.4 23.2c9.9 13.2 16.6 30.9 16.6 48.8c0 3.4-2.2 6.5-5.5 7.6s-6.9 0-8.9-2.8l0 0 0 0zm160 0l0 0-.2-.2c-.2-.2-.4-.5-.7-.9c-.6-.8-1.6-2-2.8-3.4c-2.5-2.8-6-6.6-10.2-10.3c-8.8-7.8-18.8-14-27.7-14s-18.9 6.2-27.7 14c-4.2 3.7-7.7 7.5-10.2 10.3c-1.2 1.4-2.2 2.6-2.8 3.4c-.3 .4-.6 .7-.7 .9l-.2 .2 0 0 0 0 0 0c-2.1 2.8-5.7 3.9-8.9 2.8s-5.5-4.1-5.5-7.6c0-17.9 6.7-35.6 16.6-48.8c9.8-13 23.9-23.2 39.4-23.2s29.6 10.2 39.4 23.2c9.9 13.2 16.6 30.9 16.6 48.8c0 3.4-2.2 6.5-5.5 7.6s-6.9 0-8.9-2.8l0 0 0 0 0 0z"/></svg>

```
## No non-missing values in test_observations; cannot calculate forecast score
```

---

## Basis functions &#8680; local knowledge

---

## Basis functions &#8680; local knowledge

---
## Forecasts <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="M400 406.1V288c0-13.3-10.7-24-24-24s-24 10.7-24 24V440.6c-28.7 15-61.4 23.4-96 23.4s-67.3-8.5-96-23.4V288c0-13.3-10.7-24-24-24s-24 10.7-24 24V406.1C72.6 368.2 48 315 48 256C48 141.1 141.1 48 256 48s208 93.1 208 208c0 59-24.6 112.2-64 150.1zM256 512A256 256 0 1 0 256 0a256 256 0 1 0 0 512zM159.6 220c10.6 0 19.9 3.8 25.4 9.7c7.6 8.1 20.2 8.5 28.3 .9s8.5-20.2 .9-28.3C199.7 186.8 179 180 159.6 180s-40.1 6.8-54.6 22.3c-7.6 8.1-7.1 20.7 .9 28.3s20.7 7.1 28.3-.9c5.5-5.8 14.8-9.7 25.4-9.7zm166.6 9.7c5.5-5.8 14.8-9.7 25.4-9.7s19.9 3.8 25.4 9.7c7.6 8.1 20.2 8.5 28.3 .9s8.5-20.2 .9-28.3C391.7 186.8 371 180 351.6 180s-40.1 6.8-54.6 22.3c-7.6 8.1-7.1 20.7 .9 28.3s20.7 7.1 28.3-.9zM208 320v32c0 26.5 21.5 48 48 48s48-21.5 48-48V320c0-26.5-21.5-48-48-48s-48 21.5-48 48z"/></svg>

---

## We need *global* knowledge
<img src="ASC_talk_slidedeck_files/figure-html/unnamed-chunk-7-1.svg" style="display: block; margin: auto;" />

---
## We need *global* knowledge
<img src="ASC_talk_slidedeck_files/figure-html/unnamed-chunk-8-1.svg" style="display: block; margin: auto;" />

---

## Dynamic GAMs

`$$\mathbb{E}(\boldsymbol{Y_t}|\boldsymbol{X_t})=g^{-1}(\alpha + \sum_{j=1}^{J}f(x_{jt}) + z_t)$$`

<br/>
Where: 
- `$g^{-1}$` is the inverse of the link function
- `${\alpha}$` is the intercept
- `$f(x)$` are potentially nonlinear functions of the `$J$` predictors
- `$z_t$` is a .emphasize[*latent dynamic process*]

---

## Modelling with the [`mvgam` 📦](https://github.com/nicholasjclark/mvgam/tree/master)

Bayesian framework to fit Dynamic GLMs and Dynamic GAMs
- Hierarchical intercepts, slopes and smooths
- Latent dynamic processes
- State-Space models with measurement error

Built off the [`mgcv` 📦](https://cran.r-project.org/web/packages/mgcv/index.html) to construct penalized smoothing splines

Familiar <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> formula interface

Uni- or multivariate series from a range of response distributions

Uses [Stan](https://mc-stan.org/) for ADVI, Laplace or full Hamiltonian Monte Carlo

---

class: middle center
### We can fit models that include random effects, nonlinear effects, time-varying effects and complex multidimensional smooth functions. All these effects can operate .emphasize[*on both process and observation models*]
<br>
### Can incorporate unobserved temporal dynamics; no need to regress the outcome on past values or resort to transformations
<br>
### What kinds of dynamic processes are available in the `mvgam` 📦?

---

## Piecewise linear...
<img src="ASC_talk_slidedeck_files/figure-html/unnamed-chunk-9-1.svg" style="display: block; margin: auto;" />

---

## ...or logistic with upper saturation
<img src="ASC_talk_slidedeck_files/figure-html/unnamed-chunk-10-1.svg" style="display: block; margin: auto;" />

---

## RW or ARMA(p = 1-3, q = 0-1)
<img src="ASC_talk_slidedeck_files/figure-html/unnamed-chunk-11-1.svg" style="display: block; margin: auto;" />

---

## Gaussian Process...
<img src="ASC_talk_slidedeck_files/figure-html/unnamed-chunk-12-1.svg" style="display: block; margin: auto;" />

---
## ...where length scale  &#8680; *memory*
<img src="ASC_talk_slidedeck_files/figure-html/unnamed-chunk-13-1.svg" style="display: block; margin: auto;" />

---

background-image: url('./resources/VAR.svg')
background-size: contain
## VAR1 &#8680; Granger causality

---

background-image: url('./resources/df_with_series.gif')
## Factors &#8680; induced correlations
---

## Example of the interface

```r
model <- mvgam(
  formula = y ~ 
    s(series, bs = 're') + 
    s(x0, series, bs = 're') +
    x1 +
    gp(x2) +
    te(x3, x4, bs = c('cr', 'tp')),
  data = data,
  family = poisson(),
  trend_model = AR(p = 1, ma = TRUE, cor = TRUE),
  algorithm = 'sampling',
  burnin = 500,
  samples = 500,
  chains = 4,
  parallel = TRUE)
```

---
## Produce all `Stan` code and objects

```r
code(model)
```
.small[

```
## // Stan model code generated by package mvgam
## functions {
##   /* Spectral density function of a Gaussian process
##   * with squared exponential covariance kernel
##   * Args:
##   *   l_gp: numeric eigenvalues of an SPD GP
##   *   alpha_gp: marginal SD parameter
##   *   rho_gp: length-scale parameter
##   * Returns:
##   *   numeric values of the GP function evaluated at l_gp
##   */
##   vector spd_cov_exp_quad(data vector l_gp, real alpha_gp, real rho_gp) {
##     int NB = size(l_gp);
##     vector[NB] out;
##     real constant = square(alpha_gp) * (sqrt(2 * pi()) * rho_gp);
##     real neg_half_lscale2 = -0.5 * square(rho_gp);
##     for (m in 1 : NB) {
##       out[m] = constant * exp(neg_half_lscale2 * square(l_gp[m]));
##     }
##     return out;
##   }
## }
## data {
##   int<lower=0> total_obs; // total number of observations
##   int<lower=0> n; // number of timepoints per series
##   int<lower=0> n_sp; // number of smoothing parameters
##   int<lower=0> n_series; // number of series
##   int<lower=0> num_basis; // total number of basis coefficients
##   vector[num_basis] zero; // prior locations for basis coefficients
##   matrix[total_obs, num_basis] X; // mgcv GAM design matrix
##   array[n, n_series] int<lower=0> ytimes; // time-ordered matrix (which col in X belongs to each [time, series] observation?)
##   int<lower=1> k_gp_x2_; // basis functions for approximate gp
##   vector[k_gp_x2_] l_gp_x2_; // approximate gp eigenvalues
##   array[10] int b_idx_gp_x2_; // gp basis coefficient indices
##   matrix[24, 72] S2; // mgcv smooth penalty matrix S2
##   int<lower=0> n_nonmissing; // number of nonmissing observations
##   array[n_nonmissing] int<lower=0> flat_ys; // flattened nonmissing observations
##   matrix[n_nonmissing, num_basis] flat_xs; // X values for nonmissing observations
##   array[n_nonmissing] int<lower=0> obs_ind; // indices of nonmissing observations
## }
## transformed data {
##   vector[n_series] trend_zeros = rep_vector(0.0, n_series);
## }
## parameters {
##   // raw basis coefficients
##   vector[num_basis] b_raw;
##   
##   // gp term sd parameters
##   real<lower=0> alpha_gp_x2_;
##   
##   // gp term length scale parameters
##   real<lower=0> rho_gp_x2_;
##   
##   // gp term latent variables
##   vector[k_gp_x2_] z_gp_x2_;
##   
##   // random effect variances
##   vector<lower=0>[2] sigma_raw;
##   
##   // random effect means
##   vector[2] mu_raw;
##   
##   // latent trend AR1 terms
##   vector<lower=-1.5, upper=1.5>[n_series] ar1;
##   
##   // latent trend variance parameters
##   vector<lower=0>[n_series] sigma;
##   cholesky_factor_corr[n_series] L_Omega;
##   
##   // ma coefficients
##   matrix<lower=-1, upper=1>[n_series, n_series] theta;
##   
##   // dynamic error parameters
##   array[n] vector[n_series] error;
##   
##   // smoothing parameters
##   vector<lower=0>[n_sp] lambda;
## }
## transformed parameters {
##   array[n] vector[n_series] trend_raw;
##   matrix[n, n_series] trend;
##   array[n] vector[n_series] epsilon;
##   
##   // LKJ form of covariance matrix
##   matrix[n_series, n_series] L_Sigma;
##   
##   // computed error covariance matrix
##   cov_matrix[n_series] Sigma;
##   
##   // basis coefficients
##   vector[num_basis] b;
##   b[1 : 36] = b_raw[1 : 36];
##   b[37 : 40] = mu_raw[1] + b_raw[37 : 40] * sigma_raw[1];
##   b[41 : 44] = mu_raw[2] + b_raw[41 : 44] * sigma_raw[2];
##   
##   // derived latent states
##   trend_raw[1] = error[1];
##   epsilon[1] = error[1];
##   for (i in 2 : n) {
##     // lagged error ma process
##     epsilon[i] = theta * error[i - 1];
##     
##     // full ARMA process
##     trend_raw[i] = ar1 .* trend_raw[i - 1] + epsilon[i] + error[i];
##   }
##   b[b_idx_gp_x2_] = sqrt(spd_cov_exp_quad(l_gp_x2_, alpha_gp_x2_, rho_gp_x2_))
##                     .* z_gp_x2_;
##   L_Sigma = diag_pre_multiply(sigma, L_Omega);
##   Sigma = multiply_lower_tri_self_transpose(L_Sigma);
##   for (i in 1 : n) {
##     trend[i, 1 : n_series] = to_row_vector(trend_raw[i]);
##   }
## }
## model {
##   // prior for random effect population variances
##   sigma_raw ~ student_t(3, 0, 2.5);
##   
##   // prior for random effect population means
##   mu_raw ~ std_normal();
##   
##   // prior for (Intercept)...
##   b_raw[1] ~ student_t(3, 0.7, 2.5);
##   
##   // prior for x1B...
##   b_raw[2] ~ student_t(3, 0, 2);
##   
##   // prior for gp(x2)...
##   z_gp_x2_ ~ std_normal();
##   alpha_gp_x2_ ~ student_t(3, 0, 3);
##   rho_gp_x2_ ~ inv_gamma(1.494197, 0.056607);
##   b_raw[b_idx_gp_x2_] ~ std_normal();
##   
##   // prior for te(x3,x4)...
##   b_raw[13 : 36] ~ multi_normal_prec(zero[13 : 36],
##                                      S2[1 : 24, 1 : 24] * lambda[3]
##                                      + S2[1 : 24, 25 : 48] * lambda[4]
##                                      + S2[1 : 24, 49 : 72] * lambda[5]);
##   
##   // prior (non-centred) for s(series)...
##   b_raw[37 : 40] ~ std_normal();
##   
##   // prior (non-centred) for s(x0,series)...
##   b_raw[41 : 44] ~ std_normal();
##   
##   // priors for AR parameters
##   ar1 ~ std_normal();
##   
##   // priors for smoothing parameters
##   lambda ~ normal(5, 30);
##   
##   // priors for latent trend variance parameters
##   sigma ~ student_t(3, 0, 2.5);
##   
##   // contemporaneous errors
##   L_Omega ~ lkj_corr_cholesky(2);
##   for (i in 1 : n) {
##     error[i] ~ multi_normal_cholesky(trend_zeros, L_Sigma);
##   }
##   
##   // ma coefficients
##   for (i in 1 : n_series) {
##     for (j in 1 : n_series) {
##       if (i != j) 
##         theta[i, j] ~ normal(0, 0.2);
##     }
##   }
##   {
##     // likelihood functions
##     vector[n_nonmissing] flat_trends;
##     flat_trends = to_vector(trend)[obs_ind];
##     flat_ys ~ poisson_log_glm(append_col(flat_xs, flat_trends), 0.0,
##                               append_row(b, 1.0));
##   }
## }
## generated quantities {
##   vector[total_obs] eta;
##   matrix[n, n_series] mus;
##   vector[n_sp] rho;
##   vector[n_series] tau;
##   array[n, n_series] int ypred;
##   rho = log(lambda);
##   for (s in 1 : n_series) {
##     tau[s] = pow(sigma[s], -2.0);
##   }
##   
##   // posterior predictions
##   eta = X * b;
##   for (s in 1 : n_series) {
##     mus[1 : n, s] = eta[ytimes[1 : n, s]] + trend[1 : n, s];
##     ypred[1 : n, s] = poisson_log_rng(mus[1 : n, s]);
##   }
## }
```
]

---
## Workflow in `mvgam` 📦

Fit models with splines, GPs, and multivariate dynamic processes to sets of time series; use informative priors for effective regularization

Use posterior predictive checks and Randomized Quantile residuals to assess model failures

Use `marginaleffects` 📦 to generate interpretable (and reportable) model predictions

Produce probabilistic forecasts

Evaluate forecasts from using proper scoring rules                           
---

## More resources
Cheatsheet &#8680; [Overview of `mvgam`](https://github.com/nicholasjclark/mvgam/raw/master/misc/mvgam_cheatsheet.pdf)

Vignette &#8680; [Introduction to the package](https://nicholasjclark.github.io/mvgam/articles/mvgam_overview.html)

Vignette &#8680; [Shared latent process models](https://nicholasjclark.github.io/mvgam/articles/shared_states.html)

Vignette &#8680; [Time-varying effects](https://nicholasjclark.github.io/mvgam/articles/time_varying_effects.html)

Vignette &#8680; [Multivariate State-Space models](https://nicholasjclark.github.io/mvgam/articles/trend_formulas.html)

Motivating publication &#8680; Clark & Wells 2023 [*Methods in Ecology and Evolution*](https://besjournals.onlinelibrary.wiley.com/doi/full/10.1111/2041-210X.13974)

---
## Relevant links
[`mvgam` 📦 website](https://nicholasjclark.github.io/mvgam/)

[<svg aria-hidden="true" role="img" viewBox="0 0 496 512" style="height:1em;width:0.97em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:black;overflow:visible;position:relative;"><path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"/></svg> nicholasjclark](https://github.com/nicholasjclark)

[<svg aria-hidden="true" role="img" viewBox="0 0 640 512" style="height:1em;width:1.25em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:black;overflow:visible;position:relative;"><path d="M192 96a48 48 0 1 0 0-96 48 48 0 1 0 0 96zm-8 384V352h16V480c0 17.7 14.3 32 32 32s32-14.3 32-32V192h56 64 16c17.7 0 32-14.3 32-32s-14.3-32-32-32H384V64H576V256H384V224H320v48c0 26.5 21.5 48 48 48H592c26.5 0 48-21.5 48-48V48c0-26.5-21.5-48-48-48H368c-26.5 0-48 21.5-48 48v80H243.1 177.1c-33.7 0-64.9 17.7-82.3 46.6l-58.3 97c-9.1 15.1-4.2 34.8 10.9 43.9s34.8 4.2 43.9-10.9L120 256.9V480c0 17.7 14.3 32 32 32s32-14.3 32-32z"/></svg> slides for this talk](https://github.com/nicholasjclark/ASC_talk)

[<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:black;overflow:visible;position:relative;"><path d="M352 256c0 22.2-1.2 43.6-3.3 64H163.3c-2.2-20.4-3.3-41.8-3.3-64s1.2-43.6 3.3-64H348.7c2.2 20.4 3.3 41.8 3.3 64zm28.8-64H503.9c5.3 20.5 8.1 41.9 8.1 64s-2.8 43.5-8.1 64H380.8c2.1-20.6 3.2-42 3.2-64s-1.1-43.4-3.2-64zm112.6-32H376.7c-10-63.9-29.8-117.4-55.3-151.6c78.3 20.7 142 77.5 171.9 151.6zm-149.1 0H167.7c6.1-36.4 15.5-68.6 27-94.7c10.5-23.6 22.2-40.7 33.5-51.5C239.4 3.2 248.7 0 256 0s16.6 3.2 27.8 13.8c11.3 10.8 23 27.9 33.5 51.5c11.6 26 20.9 58.2 27 94.7zm-209 0H18.6C48.6 85.9 112.2 29.1 190.6 8.4C165.1 42.6 145.3 96.1 135.3 160zM8.1 192H131.2c-2.1 20.6-3.2 42-3.2 64s1.1 43.4 3.2 64H8.1C2.8 299.5 0 278.1 0 256s2.8-43.5 8.1-64zM194.7 446.6c-11.6-26-20.9-58.2-27-94.6H344.3c-6.1 36.4-15.5 68.6-27 94.6c-10.5 23.6-22.2 40.7-33.5 51.5C272.6 508.8 263.3 512 256 512s-16.6-3.2-27.8-13.8c-11.3-10.8-23-27.9-33.5-51.5zM135.3 352c10 63.9 29.8 117.4 55.3 151.6C112.2 482.9 48.6 426.1 18.6 352H135.3zm358.1 0c-30 74.1-93.6 130.9-171.9 151.6c25.5-34.2 45.2-87.7 55.3-151.6H493.4z"/></svg> personal website](https://researchers.uq.edu.au/researcher/15140)