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\noindent Statistica Sinica {\bf 17}(2007), 667-690

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\centerline{\large\bf ADAPTIVE BAYESIAN CRITERIA IN VARIABLE}
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\centerline{\large\bf SELECTION FOR GENERALIZED LINEAR MODELS}
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\author{Xinlei Wang and Edward I.  George}
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\centerline{\it Southern Methodist University and University of
Pennsylvania}
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\begin{quotation}
\noindent {\it Abstract:}
 For the problem of variable selection in
generalized linear models, we develop various adaptive Bayesian
criteria.  Using a hierarchical mixture setup for model uncertainty,
combined with an integrated Laplace approximation, we derive
Empirical Bayes and Fully Bayes criteria that can be computed easily
and quickly.  The performance of these criteria is assessed via
simulation and compared to other criteria such as $AIC$ and $BIC$ on
normal, logistic and Poisson regression model classes.  A Fully
Bayes criterion based on a restricted region hyperprior seems to be
the most promising.  Finally, our criteria are illustrated and
compared with competitors on a data example.\par
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\noindent {\it Key words and phrases:}
AIC, BIC,
empirical Bayes, fully Bayes, hierarchical Bayes, Laplace
approximation.\par
\end{quotation}

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