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Activity Number:
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482
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Type:
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Contributed
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Date/Time:
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Thursday, August 7, 2008 : 8:30 AM to 10:20 AM
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Sponsor:
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Section on Bayesian Statistical Science
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| Abstract - #300956 |
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Title:
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Bayesian Case Influence Measures and Applications
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Author(s):
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Hyunsoon Cho*+ and Hongtu Zhu and Joseph G. Ibrahim
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Companies:
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The University of North Carolina at Chapel Hill and The University of North Carolina at Chapel Hill and The University of North Carolina at Chapel Hill
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Address:
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3920 South Roxboro Street, Apt213, Durham, NC, 27713,
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Keywords:
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Case influence measures ; Markov chain Monte Carlo ; Model complexity ; Model selection criterion ; Bayesian regression models
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Abstract:
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We introduce three types of Bayesian case influence measures based on case deletion, and propose Bayesian information criterion and goodness of fit statistics. We examine the asymptotic approximations and equivalencies of the proposed measures. We show that the sum of the proposed Bayesian case-deletion measures can measure model complexity and are associated with the effective number of parameters in deviance information criterion. We construct a Bayesian information criterion using the posterior mean of the expected log likelihood. We show that the proposed measure of model complexity can asymptotically correct the asymptotic bias of the posterior mean of the log likelihood. The proposed goodness-of-fit statistics is based on the sum of the Bayesian case-deletion measures. We illustrate the methodology using theoretical as well as numerical examples in Bayesian regression models.
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