Bayesian networks: regenerative Gibbs samplings

Abstract

Gibbs samplings is a Markov Chain Monte Carlo technique for estimating conditional probabilities in Bayesian networks. A major problem of Gibbs sampling is the dependency of the generated chain of samples. Thus the estimates are biased unless the initial value of the chain is drawn from the target distribution. One elegant method to overcome the initial bias is regenerative samplings. We reported elsewhere the “stationary minorization condition” that makes any Markov Chain Monte Carlo technique regenerative. In this paper, we show how this condition can be easily met in the simulations of any Bayesian network.

Keywords:

• Bayesian networks; Approximate inference; Gibbs samplings
• Markov Chain Monte Carlo
• regenerative