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Activity Number:
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475
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Type:
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Contributed
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Date/Time:
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Wednesday, August 1, 2007 : 2:00 PM to 3:50 PM
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Sponsor:
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IMS
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| Abstract - #309162 |
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Title:
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Gibbs Sampling for Bayesian Models
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Author(s):
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Alicia Johnson*+
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Companies:
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The University of Minnesota
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Address:
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2014 DuPont Ave S Apt 7, Minneapolis, MN, 55405,
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Keywords:
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Block Gibbs sampler ; burn-in ; geometric ergodicity ; drift condition ; minorization condition ; convergence rate
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Abstract:
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We consider a Bayesian hierarchical version of the random intercepts model. The posterior density for this model makes it difficult to find closed form solutions of integrals required for inference. For this reason, we construct a block Gibbs sampler for this model. We establish drift and minorization conditions on the underlying Markov chain and apply results from J. S. Rosenthal [J. Amer. Statist. Assoc. 90 (1995) 558-566] to construct upper bounds for the total variation distance to stationarity for the chain. Using these bounds and a prespecified desired distance to stationarity we can ensure adequate burn-in for the block Gibbs sampler.
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