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@ -27,6 +27,7 @@
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\input{../assets/preambles/BibPreamble.tex}
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\input{../assets/preambles/GeneralPreamble.tex}
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\addbibresource{/home/will/research/ClinicalTrialsPaper/Latex/assets/preambles/References.bib}
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%----------------------------------------------------------------------------------------
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% TITLE PAGE
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@ -445,19 +446,20 @@ Washington State University \\ % Your institution for the title page
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Thus the required adjustment set depends on the effects of interest.
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For the total effect these are controls for:
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For the total effect:
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\begin{itemize}
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\item Proceed with Phase III
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\item Condition
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\item Population
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\end{itemize}
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For the direct effect these are controls for:
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For the direct effect:
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\begin{itemize}
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\item Proceed with Phase III
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\item Condition
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\item Population (optional)
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\item Enrollment
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\item Enrollment Status
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\item Elapsed Duration
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\end{itemize}
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\end{frame}
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@ -736,24 +738,53 @@ Washington State University \\ % Your institution for the title page
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\begin{frame}
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\frametitle{Total Effects Model}
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%TODO: describe X\beta
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\begin{itemize}
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\item asinh(brands with identical ingredients)
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\item asinh(brands in USP-DC category)
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\item asinh(high sdi DALY estimate)
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\item asinh(high-medium sdi DALY estimate)
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\item asinh(medium sdi DALY estimate)
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\item asinh(low-medium sdi DALY estimate)
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\item asinh(low sdi DALY estimate)
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\end{itemize}
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Units of observation: Snapshots
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\end{frame}
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%-------------------------------
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\begin{frame}
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\frametitle{Direct Effects Model}
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%TODO: describe X\beta
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\begin{itemize}
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\item elapsed duration
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\item enrollment status
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\item asinh(brands with identical ingredients)
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\item asinh(brands in USP-DC category)
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\item asinh(high sdi DALY estimate)
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\item asinh(high-medium sdi DALY estimate)
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\item asinh(medium sdi DALY estimate)
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\item asinh(low-medium sdi DALY estimate)
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\item asinh(low sdi DALY estimate)
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\end{itemize}
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Units of Observation: Snapshot
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\end{frame}
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%-------------------------------
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\begin{frame}
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\frametitle{Analysis}
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Review:
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For each effect, we will look at:
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\begin{itemize}
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\item Hyperparameters
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\item Parameters of Interest
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\item Distribution of Parameters of Interest
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\item Distrbution of Predicted Differences (Hypothetical Causal Intervention)
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\end{itemize}
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\vspace{12pt}
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The interventions are:
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\begin{itemize}
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\item Adding a single brand to the generic market competitors
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\item Adding a single brand to the USP DC market competitors
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\end{itemize}
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\end{frame}
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%-------------------------------
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\begin{frame}
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@ -767,29 +798,30 @@ Washington State University \\ % Your institution for the title page
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%--------------------------------
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%-------------------------------
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\begin{frame}
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\frametitle{Priors - Mu}
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\frametitle{Data Summaries}
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\begin{figure}
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% \includegraphics[height=0.8\textheight]{../assets/img/Images/}
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\label{FIG:Prior:Mu}
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\caption{Prior - Mu}
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\includegraphics[height=0.8\textheight]{/home/will/research/ClinicalTrialsPaper/Latex/Presentation/Images/HistTrialDurations_Faceted.png}
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\end{figure}
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\end{frame}
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%-------------------------------
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\begin{frame}
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\frametitle{Priors - Sigma}
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\frametitle{Data Summaries}
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\begin{figure}
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% \includegraphics[height=0.8\textheight]{../assets/img/Images/}
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\label{FIG:Prior:Sigma}
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\caption{Prior - Sigma}
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\includegraphics[height=0.8\textheight]{/home/will/research/ClinicalTrialsPaper/Latex/Presentation/Images/HistSnapshots.png}
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\end{figure}
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\end{frame}
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%-------------------------------
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\begin{frame}
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\frametitle{Priors - $p$}
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\frametitle{Data Summaries}
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\begin{figure}
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% \includegraphics[height=0.8\textheight]{../assets/img/Images/}
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\label{FIG:Prior:p}
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\caption{Prior - $p$}
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\includegraphics[height=0.8\textheight]{/home/will/research/ClinicalTrialsPaper/Latex/Presentation/Images/SnapshotsVsDurationVsTermination.png}
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\end{figure}
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\end{frame}
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%-------------------------------
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\begin{frame}
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\frametitle{Data Summaries}
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\begin{figure}
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\includegraphics[height=0.8\textheight]{/home/will/research/ClinicalTrialsPaper/Latex/Presentation/Images/CategoryCounts.png}
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\end{figure}
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\end{frame}
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%--------------------------------
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@ -803,29 +835,96 @@ Washington State University \\ % Your institution for the title page
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% - Distributions
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% - Review Posterior Prediction for interventions
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%--------------------------------
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%%-------------------------------
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%\begin{frame}
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% \frametitle{Priors - Mu}
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% \begin{figure}
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%% \includegraphics[height=0.8\textheight]{../assets/img/Images/}
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% \label{FIG:Prior:Mu}
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% \caption{Prior - Mu}
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% \end{figure}
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%\end{frame}
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%%-------------------------------
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%\begin{frame}
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% \frametitle{Priors - Sigma}
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% \begin{figure}
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%% \includegraphics[height=0.8\textheight]{../assets/img/Images/}
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% \label{FIG:Prior:Sigma}
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% \caption{Prior - Sigma}
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% \end{figure}
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%\end{frame}
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%-------------------------------
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\begin{frame}
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\frametitle{Results}
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Because Bayesian estimation is typically done numerically, we will first
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validate convergence.
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Then we will take a look at preliminary results.
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Sampling details
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%TODO: Update
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\begin{itemize}
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\item 4 chains
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\item 2,500 warm-up, 2,500 sampling runs
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\item seed = 11021585
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\end{itemize}
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\frametitle{Priors - $p$}
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\begin{figure}
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\includegraphics[height=0.8\textheight]{/home/will/research/ClinicalTrialsPaper/Latex/Presentation/Images/TotalEffects/prior_p.png}
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\label{FIG:Prior:p}
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\caption{Prior prediction - $p$}
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\end{figure}
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\end{frame}
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%-------------------------------
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\begin{frame}
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\frametitle{Posteriors - $\beta$ Competing Brands}
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\begin{figure}
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\includegraphics[height=0.8\textheight]{/home/will/research/ClinicalTrialsPaper/Latex/Presentation/Images/TotalEffects/Parameters/1&2_generics_and_uspdc.png}
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\label{FIG:Posterior:beta-brands-total}
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\end{figure}
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\end{frame}
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%-------------------------------
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\begin{frame}
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\frametitle{Predictive Posteriors - $p$ - no intervention}
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\begin{figure}
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\includegraphics[height=0.8\textheight]{/home/will/research/ClinicalTrialsPaper/Latex/Presentation/Images/TotalEffects/posterior_p.png}
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\label{FIG:Prior:p}
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\caption{Posterior prediction - $p$}
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\end{figure}
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\end{frame}
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%-------------------------------
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\begin{frame}
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\frametitle{Posteriors - $p$ with intervention (generics)}
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\begin{figure}
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\includegraphics[height=0.8\textheight]{/home/will/research/ClinicalTrialsPaper/Latex/Presentation/Images/TotalEffects/default_p_generic_intervention_interv.png}
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\label{FIG:Prior:p-intervention_total}
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\end{figure}
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\end{frame}
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%-------------------------------
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\begin{frame}
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\frametitle{Distribution of Differences - Generics Intervention}
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\begin{figure}
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\includegraphics[height=0.8\textheight]{/home/will/research/ClinicalTrialsPaper/Latex/Presentation/Images/TotalEffects/default_p_generic_intervention_distdiff.png}
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\label{FIG:Prior:p-intervention_total}
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\end{figure}
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\end{frame}
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%-------------------------------
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\begin{frame}
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\frametitle{Distribution of Differences - Generics Intervention | By group}
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\begin{figure}
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\includegraphics[height=0.8\textheight]{/home/will/research/ClinicalTrialsPaper/Latex/Presentation/Images/TotalEffects/p_generic_intervention_histdiff_by_group.png}
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\label{FIG:Prior:p-intervention_total}
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\end{figure}
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\end{frame}
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%-------------------------------
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\begin{frame}
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\frametitle{Posteriors - $p$ with intervention (USP DC)}
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\begin{figure}
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% \includegraphics[height=0.8\textheight]{../assets/img/Images/}
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\includegraphics[height=0.8\textheight]{/home/will/research/ClinicalTrialsPaper/Latex/Presentation/Images/TotalEffects/p_uspdc_intervention_distdiff_styled.png}
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\label{FIG:Prior:p-intervention_total}
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\end{figure}
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\end{frame}
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%-------------------------------
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\begin{frame}
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\frametitle{Posteriors - $p$ with intervention (USP DC) by group}
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\begin{figure}
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\includegraphics[height=0.8\textheight]{/home/will/research/ClinicalTrialsPaper/Latex/Presentation/Images/TotalEffects/p_uspdc_intervention_distdiff_by_group.png}
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\label{FIG:Prior:p-intervention_total}
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\end{figure}
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\end{frame}
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%-------------------------------
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\begin{frame}
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\frametitle{Questions?}
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\end{frame}
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%-------------------------------
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%--------------------------------
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\subsubsection{Direct Effects}
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% - Review Parameter Values
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@ -839,14 +938,62 @@ Washington State University \\ % Your institution for the title page
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%--------------------------------
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%-------------------------------
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\begin{frame}
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\frametitle{Convergence}
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Sampling details
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%TODO: UPDATE
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\begin{itemize}
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\item 6 chains
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\item 2,500 warm-up, 2,500 sampling runs
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\item seed = 11021585
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\end{itemize}
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\frametitle{Posteriors - $\beta$ Competing Brands}
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\begin{figure}
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\includegraphics[height=0.8\textheight]{/home/will/research/ClinicalTrialsPaper/Latex/Presentation/Images/DirectEffects/Parameters/2+3_generic_and_uspdc.png}
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\label{FIG:Posterior:beta-brands-total}
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\caption{Posterior prediction - $\beta$}
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\end{figure}
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\end{frame}
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%-------------------------------
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\begin{frame}
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\frametitle{Predictive Posteriors - $p$ - no intervention}
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\begin{figure}
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\includegraphics[height=0.8\textheight]{/home/will/research/ClinicalTrialsPaper/Latex/Presentation/Images/DirectEffects/posterior_p.png}
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\label{FIG:Prior:p}
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\caption{Posterior prediction - $p$}
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\end{figure}
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\end{frame}
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%-------------------------------
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\begin{frame}
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\frametitle{Posteriors - $p$ with intervention (generics)}
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\begin{figure}
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\includegraphics[height=0.8\textheight]{/home/will/research/ClinicalTrialsPaper/Latex/Presentation/Images/DirectEffects/default_p_generic_intervention_interv.png}
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\label{FIG:Prior:p-intervention_total}
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\end{figure}
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\end{frame}
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%-------------------------------
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\begin{frame}
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\frametitle{Distribution of Differences - Generics Intervention}
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\begin{figure}
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\includegraphics[height=0.8\textheight]{/home/will/research/ClinicalTrialsPaper/Latex/Presentation/Images/DirectEffects/default_p_generic_intervention_distdiff.png}
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\label{FIG:Prior:p-intervention_total}
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\end{figure}
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\end{frame}
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%-------------------------------
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\begin{frame}
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\frametitle{Distribution of Differences - Generics Intervention | By group}
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\begin{figure}
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\includegraphics[height=0.8\textheight]{/home/will/research/ClinicalTrialsPaper/Latex/Presentation/Images/DirectEffects/p_generic_intervention_histdiff_by_group.png}
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\label{FIG:Prior:p-intervention_total}
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\end{figure}
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\end{frame}
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%-------------------------------
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\begin{frame}
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\frametitle{Posteriors - $p$ with intervention (USP DC)}
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\begin{figure}
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% \includegraphics[height=0.8\textheight]{../assets/img/Images/}
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\includegraphics[height=0.8\textheight]{/home/will/research/ClinicalTrialsPaper/Latex/Presentation/Images/DirectEffects/p_uspdc_intervention_distdiff_styled.png}
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\label{FIG:Prior:p-intervention_total}
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\end{figure}
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\end{frame}
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%-------------------------------
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\begin{frame}
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\frametitle{Posteriors - $p$ with intervention (USP DC) by group}
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\begin{figure}
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\includegraphics[height=0.8\textheight]{/home/will/research/ClinicalTrialsPaper/Latex/Presentation/Images/DirectEffects/p_uspdc_intervention_histdiff_by_group.png}
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\label{FIG:Prior:p-intervention_total}
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\end{figure}
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\end{frame}
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%-------------------------------
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\begin{frame}
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@ -865,13 +1012,27 @@ Washington State University \\ % Your institution for the title page
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\begin{enumerate}
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\item Match more trials to ICD-10 codes and Formularies
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\item Add more formularies
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\item Remove disease categories that don't exist in the data from the priors
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\item Remove disease categories that don't exist in the data.
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\item Imputing Enrollment
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\item Add covariance terms to $\beta$.
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\end{enumerate}
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Suggestions?
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\end{frame}
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%-------------------------------
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\begin{frame}
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\frametitle{Summary}
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Results Summary
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\begin{enumerate}
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\item A trial's response to adding a competitor drug depends on:
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\begin{itemize}
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\item Whether the drug is a generic or not
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\item The disease category that applies to the trial
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\end{itemize}
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The effects suggest that the enrollment pathway had a strong regulating effect.
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\item
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\end{enumerate}
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\end{frame}
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%-------------------------------
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\begin{frame}
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@ -885,75 +1046,49 @@ Washington State University \\ % Your institution for the title page
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%-------------------------------------------------------------------------------------
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%----------------------------------
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%%%%%%%%%%%%%%%%%%%% Convergence Tests
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\subsection{Convergence}
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%\subsection{Convergence}
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%----------------------------------
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%-------------------------------
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\begin{frame}
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\frametitle{Warnings}
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%TODO: UPDATE
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\begin{itemize}
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\item There were no diverging transitions.
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\item There were 15,000 transitions that exceeded max treedepth.
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Sampling efficiency is poor.
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\item All chains had low Bayesian Fraction of Missing Information.
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Some areas of the distribution were poorly explored.
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\item R-hat = $1.23$, ideal is around 1, chains did not mix well.
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|
\item Bulk and Tail Effective Sample sizes were low,
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|
suggesting mean and variance/quantile estimates will be unreliable.
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\end{itemize}
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\cite{mc-stan}
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\end{frame}
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%-------------------------------
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\begin{frame}
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\frametitle{Convergence: Mu}
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\begin{figure}
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%TODO: UPDATE
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%\includegraphics[height=0.9\textheight]{../assets/img/2023-04-11_mu_points.png}
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\label{FIG:caption}
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\caption{Hyperparameter Points Plots: Mu}
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\end{figure}
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\end{frame}
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%-------------------------------
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\begin{frame}
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\frametitle{Convergence: Sigma}
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\begin{figure}
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|
%TODO: UPDATE
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|
%\includegraphics[height=0.9\textheight]{../assets/img/2023-04-11_mu_points.png}
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\label{FIG:caption}
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\caption{Hyperparameter Points Plots: Sigma}
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\end{figure}
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\end{frame}
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|
|
%-------------------------------
|
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|
\begin{frame}[allowframebreaks]
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\frametitle{Bibliography}
|
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|
|
\printbibliography
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|
\end{frame}
|
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|
|
%-------------------------------
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|
|
\end{document}
|
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|
%=========================================
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|
|
%\begin{frame}
|
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|
% \frametitle{MarginalRevenue}
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|
|
% \frametitle{Warnings}
|
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|
|
% %TODO: UPDATE
|
|
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|
|
%
|
|
|
|
|
% \begin{itemize}
|
|
|
|
|
% \item There were no diverging transitions.
|
|
|
|
|
% \item There were 15,000 transitions that exceeded max treedepth.
|
|
|
|
|
% Sampling efficiency is poor.
|
|
|
|
|
% \item All chains had low Bayesian Fraction of Missing Information.
|
|
|
|
|
% Some areas of the distribution were poorly explored.
|
|
|
|
|
% \item R-hat = $1.23$, ideal is around 1, chains did not mix well.
|
|
|
|
|
% \item Bulk and Tail Effective Sample sizes were low,
|
|
|
|
|
% suggesting mean and variance/quantile estimates will be unreliable.
|
|
|
|
|
% \end{itemize}
|
|
|
|
|
% \cite{mc-stan}
|
|
|
|
|
%\end{frame}
|
|
|
|
|
%%-------------------------------
|
|
|
|
|
%\begin{frame}
|
|
|
|
|
% \frametitle{Convergence: Mu}
|
|
|
|
|
% \begin{figure}
|
|
|
|
|
% \tikzfig{../Assets/owned/ch8_MarginalRevenue}
|
|
|
|
|
% \includegraphics[height=\textheight]{../Assets/copyrighted/KrugmanObsterfeldMeliz_fig8-7.jpg}
|
|
|
|
|
% \label{FIG:costs}
|
|
|
|
|
% \caption{Average Cost Curve as firms enter.}
|
|
|
|
|
% %TODO: UPDATE
|
|
|
|
|
% %\includegraphics[height=0.9\textheight]{../assets/img/2023-04-11_mu_points.png}
|
|
|
|
|
% \label{FIG:caption}
|
|
|
|
|
% \caption{Hyperparameter Points Plots: Mu}
|
|
|
|
|
% \end{figure}
|
|
|
|
|
%\end{frame}
|
|
|
|
|
%-------------------------------
|
|
|
|
|
%%-------------------------------
|
|
|
|
|
%\begin{frame}
|
|
|
|
|
% \frametitle{Columns}
|
|
|
|
|
% \begin{columns}
|
|
|
|
|
% \begin{column}{0.5\textwidth}
|
|
|
|
|
% \end{column}
|
|
|
|
|
% \begin{column}{0.5\textwidth}
|
|
|
|
|
% \begin{figure}
|
|
|
|
|
% \tikzfig{../Assets/owned/ch7_EstablishedAdvantageExample2}
|
|
|
|
|
% \label{FIG:costs}
|
|
|
|
|
% \caption{Setting the Stage}
|
|
|
|
|
% \end{figure}
|
|
|
|
|
% \end{column}
|
|
|
|
|
% \end{columns}
|
|
|
|
|
% \frametitle{Convergence: Sigma}
|
|
|
|
|
% \begin{figure}
|
|
|
|
|
% %TODO: UPDATE
|
|
|
|
|
% %\includegraphics[height=0.9\textheight]{../assets/img/2023-04-11_mu_points.png}
|
|
|
|
|
% \label{FIG:caption}
|
|
|
|
|
% \caption{Hyperparameter Points Plots: Sigma}
|
|
|
|
|
% \end{figure}
|
|
|
|
|
%\end{frame}
|
|
|
|
|
% %---------------------------------------------------------------
|
|
|
|
|
%%-------------------------------
|
|
|
|
|
\begin{frame}[allowframebreaks]
|
|
|
|
|
\frametitle{Bibliography}
|
|
|
|
|
\printbibliography
|
|
|
|
|
\end{frame}
|
|
|
|
|
%-------------------------------
|
|
|
|
|
\end{document}
|
|
|
|
|
|