Blocking Gibbs sampling in the mixed inheritance model using graph theory

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Blocking Gibbs Sampling for Linkage Analysis in Large Pedigrees with Many Loops

We will apply the method of blocking Gibbs sampling to a problem of great importance and complexity -- linkage analysis. Blocking Gibbs combines exact local computations with Gibbs sampling in a way that complements the strengths of both. The method is able to handle problems with very high complexity such as linkage analysis in large pedigrees with many loops; a task that no other known method is able to handle. New developments of the method are outlined, and it is applied to a highly complex linkage problem

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 pedigree containing 20;000 individuals. We present results showing that blocking-Gibbs sampling converges much faster than plain Gibbs sampling for very complex problems. Keywords: probabilistic expert system, graphical model, Bayesian network, junction tree, pedigree analysis, Monte Carlo. 1 Introduction Over the last decade or so, fast and exact methods have been developed for computation in graphical models (Bayesian networks) of complex stochastic systems (Cannings, Thompson & Skolnick 1976, Cannings, Thompson & Skolnick 1978, Lauritzen & Spiegelhalter 1988, Shenoy & Shafer 1990, Jensen, Lauritzen & Olesen 1990, Dawid 1992, Lauritzen ..

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 pedigree containing 20;000 individuals. We present results showing that blocking-Gibbs sampling converges much faster than plain Gibbs sampling for very complex problems