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Activity Number:
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337
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Type:
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Contributed
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Date/Time:
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Tuesday, July 31, 2007 : 2:00 PM to 3:50 PM
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Sponsor:
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Section on Bayesian Statistical Science
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| Abstract - #309934 |
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Title:
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Kullback-Leibler Divergence for Design and Model Selection
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Author(s):
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Chenpin Wang*+
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Companies:
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University of Texas Health Science Center San Antonio
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Address:
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13507 Charter Bend Dr, San Antonio, TX, 78231,
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Keywords:
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Kullback-Leibler Divergence ; Fisher information ; optimal design ; model comparison
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Abstract:
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We consider two Kullback-Leibler distances (KLDs) suitable for comparing model fit or study designs in the Bayesian framework: (a) the posterior mean of a weighted KLD between the predictive distribution of a diagnostic statistic $T_n$ under a model $g$ with a correct specification of its first two moments and that under an assumed model $f$, and (b) the KLD between the posterior distributions of certain model parameters associated with $T_n$ as described in (a). We prove the asymptotic equivalence between the KLDs in (a) and (b) under certain regularity conditions and that the estimation of the first moment of $T_n$ is unbiased under the assumed $f$. Superiority of these two KLDs to both the Bayesian and frequentist D-optimal criteria is demonstrated with examples when the assumed $f$ is subject to biased estimation of the second moment of $T_n$, but not its first moment.
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