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+ \vspace{-0.5\parskip} +\begin{minted}[gray,fontsize=\footnotesize]{stan} +data { + int N; + int y[N]; +} +parameters { + real lambda; +} +model { + lambda ~ exponential(0.2); + y ~ poisson(lambda); +} +\end{minted} + \vspace{-\parskip} +\begin{minted}[fontsize=\footnotesize,highlightlines=5]{stan} +generated quantities { + real log_lik[N]; + int y_rep[N]; + for (n in 1:N) { + y_rep[n] = poisson_rng(lambda); + log_lik[n] = poisson_lpmf(y[n] | lambda); + } +} +\end{minted} +\end{frame} + +\begin{frame}{PPC for count data -- Poisson model} + + \vspace{-1\baselineskip} + \rinline/ppc_dens_overlay(y, yrep[1:50,])/ -\begin{frame}{Example: Exposure to air pollution} + \includegraphics[height=8cm]{poisson_ppc_dens_overlay.pdf} + +\end{frame} + +\begin{frame}{PPC for count data -- Poisson model} + + \vspace{-1\baselineskip} + \rinline/ppc_rootogram(y, yrep)/ + + \includegraphics[height=8cm]{poisson_ppc_rootogram.pdf} + +\end{frame} + +\begin{frame}{PPC for count data -- Poisson model} + + \vspace{-1\baselineskip} + \rinline/prop_zero <- function(x) mean(x == 0)/\\ + \rinline/ppc_stat(y, yrep, stat = "prop_zero")/ + + \includegraphics[height=7.5cm]{poisson_ppc_stat_propzero.pdf} + +\end{frame} + +\begin{frame}{PPC for count data -- hurdle truncated Poisson model} + + \vspace{-1\baselineskip} + \rinline/ppc_rootogram(y, yrep2)/ + + \includegraphics[height=8cm]{poisson2_ppc_rootogram.pdf} + +\end{frame} + +\begin{frame}{PPC for count data -- hurdle truncated Poisson model} + + \vspace{-1\baselineskip} + \rinline/prop_zero <- function(x) mean(x == 0)/\\ + \rinline/ppc_stat(y, yrep2, stat = "prop_zero")/ + + \includegraphics[height=7.5cm]{poisson2_ppc_stat_propzero.pdf} + +\end{frame} + +\begin{frame}{Prior predictive checking: Exposure to air pollution} \begin{itemize} \item Example from Jonah Gabry, Daniel Simpson, Aki Vehtari, Michael @@ -521,7 +602,7 @@ \end{frame} -\begin{frame}{Example: Exposure to air pollution} +\begin{frame}{Prior predictive checking: Exposure to air pollution} \begin{itemize} \item Direct measurements of PM 2.5 from ground monitors at 2980 @@ -536,7 +617,7 @@ \end{center} \end{frame} -\begin{frame}{Example: Exposure to air pollution} +\begin{frame}{Prior predictive checking: Exposure to air pollution} Prior predictive checking \vspace{-1\baselineskip} @@ -547,9 +628,9 @@ \end{center} \end{frame} -\begin{frame}{Example: Exposure to air pollution} +\begin{frame}{Posterior predictive checking: Exposure to air pollution} - Posterior predictive checking -- marginal predictive distributions + Marginal predictive distributions \begin{figure} \centering \begin{subfigure}{0.48\textwidth} @@ -570,10 +651,10 @@ \end{frame} -\begin{frame}{Example: Exposure to air pollution} +\begin{frame}{Posterior predictive checking: Exposure to air pollution} - Posterior predictive checking -- test statistic (skewness) +Test statistic (skewness) \begin{figure} \centering \begin{subfigure}{0.31\textwidth} @@ -595,10 +676,10 @@ \end{frame} -\begin{frame}{Example: Exposure to air pollution} +\begin{frame}{Posterior predictive checking: Exposure to air pollution} - Posterior predictive checking -- test statistic (median for groups) +Test statistic (median for groups) \begin{figure} \centering @@ -621,9 +702,11 @@ \end{frame} -\begin{frame}{Positive target} +\begin{frame}{Posterior predictive checking: Mesquite bushes} + + Positive target: normal vs log-normal model - \includegraphics[width=11cm]{mesquite_ppc.pdf}\\ + \includegraphics[width=11.5cm]{mesquite_ppc.pdf}\\ \vspace{-0.1\baselineskip} {Predicting the yields of mesquite bushes.\\ \color{gray} \footnotesize Gelman, Hill \& Vehtari (2020): Regression and Other Stories, Chapter 11.}\\ @@ -765,104 +848,21 @@ \end{minted} } \vspace{-0.25\baselineskip} - \includegraphics[height=3.6cm]{helicopter_hier_stable.pdf} + \includegraphics[height=3.6cm]{helicopter_hier_stable_2024.pdf} \vspace{-0.1\baselineskip} \only<2>{\rinline/pp_check(fit, ndraws=20)/\\ - \includegraphics[height=3.5cm]{helicopter_hier_stable_ppc_dens_overlay.pdf}} + \includegraphics[height=3.5cm]{helicopter_hier_stable_ppc_dens_overlay_2024.pdf}} \only<3>{\rinline/pp_check(fit, type="bars")/\\ - \includegraphics[height=3.5cm]{helicopter_hier_stable_ppc_bars.pdf}} + \includegraphics[height=3.5cm]{helicopter_hier_stable_ppc_bars_2024.pdf}} \only<4>{\rinline/pp_check(fit, type="bars_grouped")/\\ - \includegraphics[height=3.5cm]{helicopter_hier_stable_ppc_bars_grouped.pdf}} + \includegraphics[height=3.5cm]{helicopter_hier_stable_ppc_bars_grouped_2024.pdf}} \only<5>{with \texttt{caret::calibration()}\\ - \includegraphics[height=3.5cm]{helicopter_hier_stable_calibration.pdf}} + \includegraphics[height=3.5cm]{helicopter_hier_stable_calibration_2024.pdf}} \only<6>{with \texttt{reliabilitydiag::reliabilitydiag()}\\ - \includegraphics[height=3.5cm]{helicopter_hier_stable_reliabilitydiag.pdf}} + \includegraphics[height=3.5cm]{helicopter_hier_stable_reliabilitydiag_2024.pdf}} \end{frame} - -\begin{frame}[fragile] - \frametitle{Posterior predictive checking -- Stan code} - - \vspace{-0.2\parskip} - \begin{itemize} - \item demo demos\_rstan/ppc/poisson-ppc.Rmd - \end{itemize} - - \vspace{-0.5\parskip} -\begin{minted}[gray,fontsize=\footnotesize]{stan} -data { - int N; - int y[N]; -} -parameters { - real lambda; -} -model { - lambda ~ exponential(0.2); - y ~ poisson(lambda); -} -\end{minted} - \vspace{-\parskip} -\begin{minted}[fontsize=\footnotesize,highlightlines=5]{stan} -generated quantities { - real log_lik[N]; - int y_rep[N]; - for (n in 1:N) { - y_rep[n] = poisson_rng(lambda); - log_lik[n] = poisson_lpmf(y[n] | lambda); - } -} -\end{minted} -\end{frame} - -\begin{frame}{PPC for count data -- Poisson model} - - \vspace{-1\baselineskip} - \rinline/ppc_dens_overlay(y, yrep[1:50,])/ - - \includegraphics[height=8cm]{poisson_ppc_dens_overlay.pdf} - -\end{frame} - -\begin{frame}{PPC for count data -- Poisson model} - - \vspace{-1\baselineskip} - \rinline/ppc_rootogram(y, yrep)/ - - \includegraphics[height=8cm]{poisson_ppc_rootogram.pdf} - -\end{frame} - -\begin{frame}{PPC for count data -- Poisson model} - - \vspace{-1\baselineskip} - \rinline/prop_zero <- function(x) mean(x == 0)/\\ - \rinline/ppc_stat(y, yrep, stat = "prop_zero")/ - - \includegraphics[height=7.5cm]{poisson_ppc_stat_propzero.pdf} - -\end{frame} - -\begin{frame}{PPC for count data -- hurdle truncated Poisson model} - - \vspace{-1\baselineskip} - \rinline/ppc_rootogram(y, yrep2)/ - - \includegraphics[height=8cm]{poisson2_ppc_rootogram.pdf} - -\end{frame} - -\begin{frame}{PPC for count data -- hurdle truncated Poisson model} - - \vspace{-1\baselineskip} - \rinline/prop_zero <- function(x) mean(x == 0)/\\ - \rinline/ppc_stat(y, yrep2, stat = "prop_zero")/ - - \includegraphics[height=7.5cm]{poisson2_ppc_stat_propzero.pdf} - -\end{frame} - \begin{frame}{Further reading and examples} \begin{itemize}