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a bit reordering and added baker2009 example
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avehtari committed Oct 10, 2024
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274 changes: 159 additions & 115 deletions slides/BDA_lecture_8a.tex
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\end{frame}

\begin{frame}{Prior predictive checking: Exposure to air pollution}
\begin{frame}{Posterior predictive checking: Mesquite bushes}

\begin{itemize}
\item Example from Jonah Gabry, Daniel Simpson, Aki Vehtari, Michael
Betancourt, and Andrew Gelman (2019). Visualization in Bayesian
workflow. \url{https://doi.org/10.1111/rssa.12378}
\item Estimation of human exposure to air pollution from particulate
matter measuring less than 2.5 microns in diameter ($\mathrm{PM}_{2.5}$)
\begin{itemize}
\item Exposure to $\mathrm{PM}_{2.5}$ is linked to a number of
poor health outcomes and a recent report estimated that
$\mathrm{PM}_{2.5}$ is responsible for three million deaths
worldwide each year (Shaddick et al., 2017)
\item In order to estimate the public health effect of ambient
$\mathrm{PM}_{2.5}$, we need a good estimate of the
$\mathrm{PM}_{2.5}$ concentration at the same spatial resolution
as our population estimates.
\end{itemize}
\end{itemize}
Positive target: normal vs log-normal model

\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.}\\

\end{frame}

\begin{frame}{Prior predictive checking: Exposure to air pollution}
\begin{frame}[fragile]{Meta-analysis}
\framesubtitle{Pharmacologic treatments for chronic obstructive pulmonary disease}

\begin{itemize}
\item Direct measurements of PM 2.5 from ground monitors at 2980
locations
\item High-resolution satellite data of aerosol optical depth

\end{itemize}
\begin{center}
\only<1>{\vspace{-1.8\baselineskip}\includegraphics[height=7cm]{map-data.png}}
\only<2>{\vspace{-1.8\baselineskip}\includegraphics[height=7cm]{plot1.png}}
\only<3>{\hspace{-3cm}\includegraphics[height=6.55cm]{plot2.png}}
\end{center}
\end{frame}
\begin{minipage}[t][][t]{1.2\linewidth}
\hspace{-10mm}
\includegraphics[width=12.5cm]{baker2009_treatments_and_studies.pdf}
\end{minipage}

\begin{frame}{Prior predictive checking: Exposure to air pollution}

Prior predictive checking
\vspace{-1\baselineskip}
\begin{center}
\only<1>{\includegraphics[width=11cm]{pm25_pp1a.pdf}}
\only<2>{\includegraphics[width=11cm]{pm25_pp1b.pdf}}
\only<3>{\includegraphics[width=11cm]{pm25_pp2.pdf}}
\end{center}
\end{frame}

\begin{frame}{Posterior predictive checking: Exposure to air pollution}

Marginal predictive distributions
\begin{figure}
\centering
\begin{subfigure}{0.48\textwidth}
\includegraphics[width=\textwidth]{ppc_dens1.png}
\caption{Model 1}
\end{subfigure}
~
\begin{subfigure}{0.48\textwidth}
\includegraphics[width=\textwidth]{ppc_dens2.png}
\caption{Model 2}
\end{subfigure}
% ~
% \begin{subfigure}{0.31\textwidth}
% \includegraphics[width=\textwidth]{ppc_dens3.png}
% \caption{Model 3}
% \end{subfigure}
\end{figure}

\end{frame}

\begin{frame}{Posterior predictive checking: Exposure to air pollution}
\begin{frame}[fragile]{Posterior predictive checking}
\framesubtitle{Pharmacologic treatments for chronic obstructive pulmonary disease}

\vspace{-0.75\baselineskip}
Pooled over studies, separate for treatments

Test statistic (skewness)
\begin{figure}
\centering
\begin{subfigure}{0.31\textwidth}
\includegraphics[width=\textwidth]{ppc_skew1.png}
\caption{Model 1}
\end{subfigure}
~
\begin{subfigure}{0.31\textwidth}
\includegraphics[width=\textwidth]{ppc_skew2.png}
\caption{Model 2}
\end{subfigure}
~
\begin{subfigure}{0.31\textwidth}
\includegraphics[width=\textwidth]{ppc_skew3.png}
\caption{Model 3}
\end{subfigure}

\end{figure}
\vspace{-0.25\baselineskip}
\begin{minted}[fontsize=\footnotesize,escapeinside=\%\%]{r}
fit_pooled <- brm(exac | trials(total) ~ %\highlight{0 + treatment}%,
prior = prior(student_t(7, 0, 1.5), class='b'),
family=binomial(), data=dat.baker2009)
\end{minted}
\vspace{-0.25\baselineskip}
\includegraphics[width=9cm]{baker2009_pooled_studies_ppc_dens_overlay.pdf}

\end{frame}

\begin{frame}{Posterior predictive checking: Exposure to air pollution}


Test statistic (median for groups)
\begin{frame}[fragile]{Posterior predictive checking}
\framesubtitle{Pharmacologic treatments for chronic obstructive pulmonary disease}

\begin{figure}
\centering
\begin{subfigure}{.31\textwidth}
\includegraphics[width=\textwidth]{ppc_med_grouped1.png}
\caption{Model 1}
\end{subfigure}
~
\begin{subfigure}{.31\textwidth}
\includegraphics[width=\textwidth]{ppc_med_grouped2.png}
\caption{Model 2}
\end{subfigure}
~
\begin{subfigure}{.31\textwidth}
\includegraphics[width=\textwidth]{ppc_med_grouped3.png}
\caption{Model 3}
\end{subfigure}
\vspace{-0.75\baselineskip}
Hirerachical for studies, hierarchical for treatments

\end{figure}

\end{frame}

\begin{frame}{Posterior predictive checking: Mesquite bushes}

Positive target: normal vs log-normal model

\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.}\\
\vspace{-0.25\baselineskip}
\begin{minted}[fontsize=\footnotesize,escapeinside=\%\%]{r}
fit_hier <- brm(exac | trials(total) ~ %\highlight{(1 | treatment) + (1 | study)}%,
family=binomial(), data=dat.baker2009)
%\phantom{~}%
\end{minted}
\vspace{-0.25\baselineskip}
\includegraphics[width=9cm]{baker2009_hier1_ppc_dens_overlay.pdf}

\end{frame}

Expand Down Expand Up @@ -871,6 +793,128 @@

\end{frame}

\begin{frame}{Prior predictive checking: Exposure to air pollution}

\begin{itemize}
\item Example from Jonah Gabry, Daniel Simpson, Aki Vehtari, Michael
Betancourt, and Andrew Gelman (2019). Visualization in Bayesian
workflow. \url{https://doi.org/10.1111/rssa.12378}
\item Estimation of human exposure to air pollution from particulate
matter measuring less than 2.5 microns in diameter ($\mathrm{PM}_{2.5}$)
\begin{itemize}
\item Exposure to $\mathrm{PM}_{2.5}$ is linked to a number of
poor health outcomes and a recent report estimated that
$\mathrm{PM}_{2.5}$ is responsible for three million deaths
worldwide each year (Shaddick et al., 2017)
\item In order to estimate the public health effect of ambient
$\mathrm{PM}_{2.5}$, we need a good estimate of the
$\mathrm{PM}_{2.5}$ concentration at the same spatial resolution
as our population estimates.
\end{itemize}
\end{itemize}

\end{frame}

\begin{frame}{Prior predictive checking: Exposure to air pollution}

\begin{itemize}
\item Direct measurements of PM 2.5 from ground monitors at 2980
locations
\item High-resolution satellite data of aerosol optical depth

\end{itemize}
\begin{center}
\only<1>{\vspace{-1.8\baselineskip}\includegraphics[height=7cm]{map-data.png}}
\only<2>{\vspace{-1.8\baselineskip}\includegraphics[height=7cm]{plot1.png}}
\only<3>{\hspace{-3cm}\includegraphics[height=6.55cm]{plot2.png}}
\end{center}
\end{frame}

\begin{frame}{Prior predictive checking: Exposure to air pollution}

Prior predictive checking
\vspace{-1\baselineskip}
\begin{center}
\only<1>{\includegraphics[width=11cm]{pm25_pp1a.pdf}}
\only<2>{\includegraphics[width=11cm]{pm25_pp1b.pdf}}
\only<3>{\includegraphics[width=11cm]{pm25_pp2.pdf}}
\end{center}
\end{frame}

% \begin{frame}{Posterior predictive checking: Exposure to air pollution}

% Marginal predictive distributions
% \begin{figure}
% \centering
% \begin{subfigure}{0.48\textwidth}
% \includegraphics[width=\textwidth]{ppc_dens1.png}
% \caption{Model 1}
% \end{subfigure}
% ~
% \begin{subfigure}{0.48\textwidth}
% \includegraphics[width=\textwidth]{ppc_dens2.png}
% \caption{Model 2}
% \end{subfigure}
% % ~
% % \begin{subfigure}{0.31\textwidth}
% % \includegraphics[width=\textwidth]{ppc_dens3.png}
% % \caption{Model 3}
% % \end{subfigure}
% \end{figure}

% \end{frame}

% \begin{frame}{Posterior predictive checking: Exposure to air pollution}


% Test statistic (skewness)
% \begin{figure}
% \centering
% \begin{subfigure}{0.31\textwidth}
% \includegraphics[width=\textwidth]{ppc_skew1.png}
% \caption{Model 1}
% \end{subfigure}
% ~
% \begin{subfigure}{0.31\textwidth}
% \includegraphics[width=\textwidth]{ppc_skew2.png}
% \caption{Model 2}
% \end{subfigure}
% ~
% \begin{subfigure}{0.31\textwidth}
% \includegraphics[width=\textwidth]{ppc_skew3.png}
% \caption{Model 3}
% \end{subfigure}

% \end{figure}

% \end{frame}

% \begin{frame}{Posterior predictive checking: Exposure to air pollution}


% Test statistic (median for groups)

% \begin{figure}
% \centering
% \begin{subfigure}{.31\textwidth}
% \includegraphics[width=\textwidth]{ppc_med_grouped1.png}
% \caption{Model 1}
% \end{subfigure}
% ~
% \begin{subfigure}{.31\textwidth}
% \includegraphics[width=\textwidth]{ppc_med_grouped2.png}
% \caption{Model 2}
% \end{subfigure}
% ~
% \begin{subfigure}{.31\textwidth}
% \includegraphics[width=\textwidth]{ppc_med_grouped3.png}
% \caption{Model 3}
% \end{subfigure}

% \end{figure}

% \end{frame}

\begin{frame}{Further reading and examples}

\begin{itemize}
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