Use of the Gibbs sampler in expert systems

摘要

The use of the Gibbs sampler as an alternative to other methods of performing calculations on a (Bayesian) belief network is surveyed, with reference to similar work in statistical analysis of genetic pedigrees. This Monte Carlo technique is one of many such methods which generate a Markov chain with a specified stationary distribution. If the distribution of the belief network is strictly positive, then convergence of the Gibbs sampler follows; however, the weaker condition of irreducibility is all that is necessary for convergence. Practical implications of these requirements are discussed, with illustrations. Methods for assessing the variability of estimates produced by the Gibbs sampler are described.