Minor

paper/appendix.tex

@@ -176,7 +176,7 @@ The coefficients for the unobserved confounder \unobservable were bounded to the
 \end{align}
 
 The intercepts for the %\judgeAmount 
-decision makers in the data and outcome \outcome were defined to have hierarchical Gaussian priors with variances $\sigma_\decision^2$ and $\sigma_\outcome^2$. The decision makers were given a joint variance parameter $\sigma_\decision^2$.
+decision makers in the data and outcome \outcome had hierarchical Gaussian priors with variances $\sigma_\decision^2$ and $\sigma_\outcome^2$. The decision makers had a joint variance parameter $\sigma_\decision^2$.
 \begin{align}
 \sigma_\decision^2, ~\sigma_\outcome^2 \sim N_+(0, \tau^2),\quad
 \alpha_\judgeValue \sim N(0, \sigma_\decision^2),\quad

paper/experiments.tex

@@ -41,7 +41,7 @@ A decision $\decision$ is made for each case by the assigned decision maker.
 %
 The exact method of assigning a decision is specified in the next subsection (Sec.~\ref{sec:dm_exps}).
 %
-If the decision is positive, then a binary outcome is sampled from a Bernoulli distribution to the case so that
+If the decision is positive, then a binary outcome is sampled from a Bernoulli distribution:
 \begin{equation}
 \prob{\outcome = 0~|~\decision=1, \obsFeaturesValue, \unobservableValue}  =  \invlogit(b_\obsFeatures \obsFeaturesValue + b_\unobservable \unobservableValue + e_\outcome)  \label{eq:Ysampling} 
 \end{equation}% Note the ''inverted'' probability and added \epsilon_\outcome compared to eq 1.
@@ -76,7 +76,7 @@ We describe both of them below.
 %
 The decisions of decision makers \humanset are based on their perception of the dangerousness of a case, to which we refer as the {\it risk score}.
 %
-With synthetic data we compute the risk score so that
+With synthetic data we compute the risk score as
 \begin{equation} \label{eq:risk}
 \text{risk score} = b_\obsFeatures \obsFeatures + b_\unobservable \unobservable.
 \end{equation}