Geometric Ergodicity of Gibbs Samplers for Bayesian General Linear Mixed Models with Proper Priors

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Geometric Ergodicity of Gibbs Samplers for Bayesian General Linear Mixed Models with Proper Priors (2013)

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by Jorge Carlos Román , James P. Hobert

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BibTeX

@MISC{Román13geometricergodicity,
    author = {Jorge Carlos Román and James P. Hobert},
    title = {Geometric Ergodicity of Gibbs Samplers for Bayesian General Linear Mixed Models with Proper Priors},
    year = {2013}
}

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Abstract

When a Bayesian version of the general linear mixed model is created by adopting a condi-tionally conjugate prior distribution, a simple block Gibbs sampler can be employed to explore the resulting intractable posterior density. In this article it is shown that, under mild conditions that nearly always hold in practice, the block Gibbs Markov chain is geometrically ergodic. 1

Keyphrases

bayesian general linear mixed model proper prior geometric ergodicity gibbs sampler block gibbs markov chain general linear mixed model simple block gibbs sampler intractable posterior density bayesian version condi-tionally conjugate prior distribution mild condition

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