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authorStratis Ioannidis <stratis@stratis-Latitude-E6320.(none)>2013-07-07 14:18:31 -0700
committerStratis Ioannidis <stratis@stratis-Latitude-E6320.(none)>2013-07-07 14:18:31 -0700
commit240bbb99052ea5e873128649d01228442d889a33 (patch)
treefcf837b20c529980e16b6184b85828285d4c4a4b /problem.tex
parentde9f4d9820ce6a879bcc82f25334510e013f052d (diff)
downloadrecommendation-240bbb99052ea5e873128649d01228442d889a33.tar.gz
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@@ -54,8 +54,7 @@ Maximizing $I(\beta;y_S)$ is therefore equivalent to maximizing $\log\det(R+ \T{
$D$-optimality criterion
\cite{pukelsheim2006optimal,atkinson2007optimum,chaloner1995bayesian}.
-Note that the estimator $\hat{\beta}$ is a linear map of $y_S$. As $y_S$ is a multidimensional normal r.v., so is $\hat{\beta}$; in particular, $\hat{\beta}$ has
-covariance $\sigma^2(R+\T{X_S}X_S)^{-1}$. As such, maximizing $I(\beta;y_S)$ can alternatively be seen as a means of reducing the uncertainty on estimator $\hat{\beta}$ by minimizing the product of the eigenvalues of its covariance (as the latter equals the determinant).
+%Note that the estimator $\hat{\beta}$ is a linear map of $y_S$. As $y_S$ is a multidimensional normal r.v., so is $\hat{\beta}$; in particular, $\hat{\beta}$ has covariance $\sigma^2(R+\T{X_S}X_S)^{-1}$. As such, maximizing $I(\beta;y_S)$ can alternatively be seen as a means of reducing the uncertainty on estimator $\hat{\beta}$ by minimizing the product of the eigenvalues of its covariance (as the latter equals the determinant).
%An alternative interpretation, given that $(R+ \T{X_S}X_S)^{-1}$ is the covariance of the estimator $\hat{\beta}$, is that it tries to minimize the
%which is indeed a function of the covariance matrix $(R+\T{X_S}X_S)^{-1}$.