diff --git a/paper/imputation.tex b/paper/imputation.tex index 344946443e98efd496baad652ab06c706fc9498a..5542c82c50d3f320585edcf1aa369f7b7280af96 100644 --- a/paper/imputation.tex +++ b/paper/imputation.tex @@ -209,10 +209,7 @@ Formally, we obtain \begin{equation} \prob{\parameters | \dataset} = \frac{\prob{\dataset | \parameters} \prob{\parameters}}{\prob{\dataset}} . \end{equation} -% -In practice, we use the MCMC functionality of Stan\footnote{\url{https://mc-stan.org/}} to obtain a sample \sample of this posterior distribution, where each element of \sample contains one instance of parameters \parameters. -% -Sample \sample can now be used to compute various probabilistic quantities of interest, including a (posterior) distribution of \unobservable for each entry in dataset \dataset. + \spara{Computing counterfactuals} Having obtained a posterior probability distribution for parameters \parameters in parameter space \parameterSpace, we can now expand expression~(\ref{eq:counterfactual}) as follows. @@ -256,6 +253,12 @@ Having obtained outcome estimates for data entries with $\decision_\human = 0$ a % Our approach is summarized in Figure~\ref{fig:approach}. +\spara{Implementation} +% +In practice, we use the MCMC functionality of Stan\footnote{\url{https://mc-stan.org/}} to obtain a sample \sample of this posterior distribution, where each element of \sample contains one instance of parameters \parameters. +% +Sample \sample can now be used to compute various probabilistic quantities of interest, including a (posterior) distribution of \unobservable for each entry in dataset \dataset. + %Original by Michael and Riku %\subsection{Model definition} \label{sec:model_definition} %