From 90ab23662cbdc75186c976c158b75c9559602f44 Mon Sep 17 00:00:00 2001
From: Antti Hyttinen <ajhyttin@gmail.com>
Date: Tue, 7 Jan 2020 12:25:23 +0200
Subject: [PATCH] ...
---
paper/imputation.tex | 11 +++++++----
1 file changed, 7 insertions(+), 4 deletions(-)
diff --git a/paper/imputation.tex b/paper/imputation.tex
index 3449464..5542c82 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}
%
--
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