Blocking Gibbs sampling in very large probabilistic expert systems

We introduce a methodology for performing approximate computations in very complex probabilistic systems (e.g. huge pedigrees). Our approach, called blocking Gibbs, combines exact local computations with Gibbs sampling in a way that complements the strengths of both. The methodology is illustrated on a real-world problem involving a heavily inbred pedigreee containing 20 000 individuals. We present results showing that blocking-Gibbs sampling converges much faster than plain Gibbs sampling for very complex problems.