diff --git a/paper/imputation.tex b/paper/imputation.tex
index c236852280cb5fc82cdbb852acd3afe392342d3b..5ea43b965677b7bcd5d4de56d902cd2f1f913c85 100644
--- a/paper/imputation.tex
+++ b/paper/imputation.tex
@@ -137,8 +137,8 @@ Since the decision are ultimately based on the risk factors for behaviour, we mo
 \begin{equation}
 \prob{\decision_{\human} = 0~|~\leniencyValue_\human,\obsFeaturesValue, \unobservableValue}  =  \invlogit(\alpha_\human + \gamma_\obsFeaturesValue\obsFeaturesValue + \gamma_\unobservableValue \unobservableValue + \epsilon_\decisionValue)  \label{eq:judgemodel} 
 \end{equation}%
-Note that index $j$ refers to decision maker $\human$. Parameter $\alpha_\human$ provides for the leniency of a decision maker by $\logit(\leniencyValue_\human)$. 
-Note that we are making the simplifying assumption that coefficients $\gamma$ are the same for all defendants, but decision makers are allowed to differ in intercept $\alpha_j \approx \logit(\leniencyValue_j)$ so as to model varying leniency levels among them. % (Eq. \ref{eq:leniencymodel}).
+Intercept $\alpha_\human$ provides for the leniency of a decision maker $\human$ by $\logit(\leniencyValue_\human)$. 
+Note that we are making the simplifying assumption that coefficients $\gamma$ are the same for all defendants, but decision makers are allowed to differ in intercept $\alpha_\human \approx \logit(\leniencyValue_\human)$ so as to model varying leniency levels among them. % (Eq. \ref{eq:leniencymodel}).
 
 %The decision makers in the data differ from each other only by leniency.
 %\noindent
@@ -219,7 +219,7 @@ We use prior distributions given in Appendix~X to ensure the identifiability of
 
 %\spara{Computing counterfactuals} 
 For the model defined above, the counterfactual $\hat{Y}$ can be computed by the approach of Pearl.
-For fully defined model (fixed parameters)  $\hat{Y}$ can be determined by the following expression:
+For fully defined model (fixed parameters)  the counterfactual expectation can be determined by the following expression:
 %\begin{align}
 %\cfoutcome & = \int   \prob{\outcome=1|\decision=1,\obsFeaturesValue,\unobservableValue}   \prob{z|\leniency=\leniencyValue, \decision_{\human} =0, \obsFeaturesValue}\diff{\unobservableValue}
 %\end{align}