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Activity Number:
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351
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Type:
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Invited
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Date/Time:
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Tuesday, August 4, 2009 : 2:00 PM to 3:50 PM
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Sponsor:
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IMS
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| Abstract - #302755 |
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Title:
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Posterior Normality and Prior Selection in High Dimensions
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Author(s):
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Bertrand Clarke*+ and Subhashis Ghoshal
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Companies:
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The University of British Columbia/University of Miami and North Carolina State University
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Address:
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6356 Agricultural Rd Rm 333, Vancouver, BC, V6T 1Z2, Canada
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Keywords:
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posterior normality ; objective prior ; Jeffreys prior ; relative entropy
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Abstract:
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When the dimension of a parameter is increasing as a function of sample size, the main techniques for proving asymptotic normality of the posterior continue to give that Jeffreys prior remains least favorable under entropy loss. The main hypotheses are that the likelihood is an IID smooth exponential family and that $p=p(n)$ does not increase too quickly. Separate from deriving the Jeffreys prior, it is important to verify that using the Jeffreys prior results in an asymptotically well-behaved posterior. We derive Jeffreys prior in the increasing $p$ case for the multinomial and normal families and verify that the posterior is well-behaved. The techniques of proof suggest extensions to include nuisance parameters are possible and the information-theoretic interpretation gives implications for Shannon coding theory.
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