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Activity Number:
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541
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Type:
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Contributed
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Date/Time:
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Thursday, August 2, 2007 : 10:30 AM to 12:20 PM
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Sponsor:
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Section on Bayesian Statistical Science
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| Abstract - #309304 |
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Title:
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Nonparametric Hierarchical Bayes Analysis of Binomial Data Using Berstein Polynomials
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Author(s):
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Tingting Zhang*+ and Jun S. Liu
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Companies:
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Harvard University and Harvard University
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Address:
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1 Oxford Street 608, Cambridge, MA, 02138,
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Keywords:
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Nonparametric Bayesian inference ; Bernstein-DirichletBernstein-Dirichlet priors ; Dirichlet process ; Gibbs sampler
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Abstract:
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We propose a Bayesian nonparametric procedure for density estimation of binomial data with Bernstein-Dirichlet prior which is based on Bernstein polynomials. The predictive density is expressed as a weighted mixture of beta densities. This indicates that the predictive density is smooth everywhere, which is an improvement over the previous nonparametric Bayesian estimate with Dirichlet prior. The comparison between our approach and a previous nonparametric approach is provided through examples, and we find that Bernstein estimates are more robust to the sample variation than estimates with Dirichlet prior. Analysis of the bating data of Efron and Morris and the tack data of Beckett and Diaconis, which motivated this study, is supplemented to illustrate our method.
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