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Activity Number:
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524
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Type:
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Contributed
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Date/Time:
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Wednesday, August 5, 2009 : 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 - #304880 |
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Title:
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Consistency in Multivariate Bayesian Density Estimation
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Author(s):
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Subhashis Ghoshal*+ and Yuefeng Wu
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Companies:
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North Carolina State University and North Carolina State University
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Address:
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2501 Founders Dr, Raleigh, NC, 27695,
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Keywords:
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Dirichlet mixture ; multivariate normal kernel ; density estimation ; Kullback-Leibler property ; entropy ; sieves
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Abstract:
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We consider the problem of density estimation in higher dimension from the Bayesian point of view using Dirichlet mixture of multivariate normal kernel. The scale of the kernel may be a scalar of a matrix. MCMC methods for posterior computation have been developed in the literature. Posterior consistency and rate of convergence results were established earlier in one dimension. In this talk, we discuss extensions of these results to higher dimension using general theorems on posterior consistency which relies on prior positivity in Kullback-Leibler sense and bounds for entropy of sieves for the space of the densities. A subtle estimate of the posterior probability of the complement of the sieve, which uses special properties of Dirichlet mixture, is developed. Explicit sufficient conditions are studied for normal base measure and (truncated) inverse gamma/Wishart type prior on the scale.
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