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Paper No. 11-21

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RJB Goudie and S Mukherjee

An efficient Gibbs sampler for structural inference in Bayesian networks

Date: June 2011

Abstract: We propose a Gibbs sampler for structural inference in Bayesian networks. The standard Markov chain Monte Carlo (MCMC) algorithms used for this problem are random-walk Metropolis-Hastings samplers, but for problems of even moderate dimension, these samplers often exhibit slow mixing. The Gibbs sampler proposed here conditionally samples the complete set of parents of a node in a single move, by blocking together particular components. These blocks can themselves be paired together to improve the efficiency of the sampler. The conditional distribution used for sampling can be viewed as a posterior distribution for a constrained Bayesian variable selection for the parents of a node. This view sheds further light on the increasingly well understood connection between Bayesian variable selection and structural inference. We empirically examine the performance of the sampler using data simulated from the ALARM network.