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.
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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.
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@@ -256,6 +253,12 @@ Having obtained outcome estimates for data entries with $\decision_\human = 0$ a
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Our approach is summarized in Figure~\ref{fig:approach}.
\spara{Implementation}
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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.