From dacff6f8d498ef281066742305db90d1121d7f3b Mon Sep 17 00:00:00 2001
From: Stratis Ioannidis <stratis@stratis-Latitude-E6320.(none)>
Date: Tue, 30 Oct 2012 08:26:46 -0700
Subject: ?

---
 problem.tex | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

(limited to 'problem.tex')

diff --git a/problem.tex b/problem.tex
index 3faef3b..c3fd38f 100644
--- a/problem.tex
+++ b/problem.tex
@@ -2,7 +2,7 @@
 In the context of experimental design, an \emph{experiment} is a random variable $E$ sampled from a distribution $P_\beta$, where $\beta\in \Omega$ is an unknown parameter. An experimenter wishes to learn parameter $\beta$, and can chose among a set of possible different experiments, all of which have distributions parametrized by the same $\beta$. 
 
 The problem of optimal experimental design amounts to determining an experiment that maximizes the information revealed about parameter $\beta$. 
-Though a variety of different measures of information exist in literature (see, \emph{e.g.}, \cite{ginebra}), the so-called \emph{value of information} \cite{lindley} is commonly used in traditional Bayesian experimental design  \cite{lindley}. In particular, in the Bayesian setup, it is assumed that $\beta$ is sampled from a well-known prior distribution. The value of an experiment $E$ is then defined as the expected change in the entropy of $\beta$ (\emph{i.e.}, the mutual information between $E$ an $\beta$), given by
+Though a variety of different measures of information exist in literature (see, \emph{e.g.}, \cite{ginebra,chaloner}), the so-called \emph{value of information} \cite{lindley} is commonly used in traditional Bayesian experimental design. In particular, in the Bayesian setup, it is assumed that $\beta$ is sampled from a well-known prior distribution. The value of an experiment $E$ is then defined as the expected change in the entropy of $\beta$ (\emph{i.e.}, the mutual information between $E$ an $\beta$), given by
 \begin{align}
  \mutual(\beta; E) =  \entropy(\beta) - \entropy(\beta \mid E).\label{voi}
 \end{align} 
@@ -27,7 +27,7 @@ Learning $\beta$ has many interesting applications, that make linear regression
 In the Bayesian setting,  
 it is commonly assumed that $\beta$  follows a
 multivariate normal distribution of mean zero and covariance matrix $\sigma_1^2
-I_d$. Under this prior and the linear model \eqref{model}, the value of information \eqref{voi} of an experiment $Y_S$ is given by \cite{...}
+I_d$. Under this prior and the linear model \eqref{model}, the value of information \eqref{voi} of an experiment $Y_S$ is given by \cite{boyd,chaloner}
     \begin{align}\label{vs}
         V(S)
         & \defeq I(\beta;y_S) = \frac{1}{2}\log\det\left(I_d
-- 
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