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Gibbs sampling for Bayesian non-conjugate and hierarchical models by using auxiliary variables

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Abstract:

We demonstrate the use of auxiliary (or latent) variables for sampling non-standard densities which arise in the context of the Bayesian analysis of non-conjugate and hierarchical models by using a Gibbs sampler. Their strategic use can result in a Gibbs sampler having easily sampled full conditionals. We propose such a procedure to simplify or speed up the Markov chain Monte Carlo algorithm. The strength of this approach lies in its generality and its ease of implementation. The aim of the paper, therefore, is to provide an alternative sampling algorithm to rejection-based methods and other sampling approaches such as the Metropolis–Hastings algorithm.

Keywords: Gibbs sampler; Hierarchical model; Latent variable; Non-conjugate model

Document Type: Original Article

DOI: http://dx.doi.org/10.1111/1467-9868.00179

Affiliations: 1: University of Michigan, Ann Arbor, USA, 2: Imperial College School of Medicine at St Mary's, London, UK, 3: Imperial College of Science, Technology and Medicine, London, UK

Publication date: April 1, 1999

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