From 55809604c10dcd4ace71079ed8d72a1ca1a5a9eb Mon Sep 17 00:00:00 2001
From: Stratis Ioannidis <stratis@stratis-Latitude-E6320.(none)>
Date: Sat, 3 Nov 2012 23:30:03 -0700
Subject: intro

---
 general.tex | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

(limited to 'general.tex')

diff --git a/general.tex b/general.tex
index 12e01a5..589b176 100644
--- a/general.tex
+++ b/general.tex
@@ -10,7 +10,7 @@ The experimenter estimates $\beta$ through \emph{maximum a posteriori estimation
 This optimization, commonly known as \emph{ridge regression}, includes an additional penalty term compared to the least squares estimation \eqref{leastsquares}.
 
 
-Let $\entropy(\beta)$ be the entropy of $\beta$ under this distribution, and $\entropy(\beta\mid y_S)$ the  entropy of $\beta$ conditioned on the experiment outcomes $Y_S$, for some $S\subseteq \mathcal{N}$. In this setting, a natural objective to select a set of experiments $S$ that maximizes her \emph{information gain}:
+Let $\entropy(\beta)$ be the entropy of $\beta$ under this distribution, and $\entropy(\beta\mid y_S)$ the  entropy of $\beta$ conditioned on the experiment outcomes $Y_S$, for some $S\subseteq \mathcal{N}$. In this setting, a natural objective, originally proposed by Lindley \cite{lindley1956measure}, is to select a set of experiments $S$ that maximizes her \emph{information gain}:
 $$ I(\beta;y_S) = \entropy(\beta)-\entropy(\beta\mid y_S). $$
 
 Assuming normal noise variables, the information gain is  equal (up to a constant) to the following value function \cite{chaloner1995bayesian}:
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