Statistical applications in fields such as bioinformatics, information retrieval, speech processing, image processing and communications often involve large-scale models in which thousands or millions of random variables are linked in complex ways. Graphical models provide a general methodology for approaching these problems, and indeed many of the models developed by researchers in these applied fields are instances of the general graphical model formalism. We review some of the basic ideas underlying graphical models, including the algorithmic ideas that allow graphical models to be deployed in large-scale data analysis problems. We also present examples of graphical models in bioinformatics, error-control coding and language processing. Key words and phrases: Probabilistic graphical models, junction tree algorithm, sum-product algorithm, Markov chain Monte Carlo, variational inference, bioinformatics, error-control coding.

missense mutations of disease genes

This paper introduces graphical models as a natural environment in which to formulate and solve problems in genetics and related areas. Particular emphasis is given to the relationships among various local computation algorithms which have been developed within the hitherto mostly separate areas of graphical models and genetics. The potential of graphical models is explored and illustrated through a number of example applications where the genetic element is substantial or dominating.

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. Keywords: Bayesian network, junction tree, pedigree analysis, Markov chain Monte Carlo, Gibbs sampling, loops, inbreeding 1 Introduction For linkage analysis - the problem of estimating the relative positions of the genes on the chromosomes - many methods have been developed over recent years. Fast and exact methods for computation in Bayesian networks (e.g., pedigrees) (Cannings, Thompson & Skolnick 1976; Pearl 1986; Lauritzen & Spiegelhalter 1988; Shenoy & Shafer 1990; Lauri...

The problem of multilocus linkage analysis is expressed as a graphical model, making explicit a previously implicit connection, and recent developments in the field are described in this context. A novel application of blocked Gibbs sampling for Bayesian networks is developed to generate inheritance matrices from an irreducible Markov chain. This is used as the basis for reconstruction of historical meiotic states and approximate calculation of the likelihood function for the location of an unmapped genetic trait. We believe this to be the only approach that currently makes fully informative multilocus linkage analysis possible on large extended pedigrees.

Running Tile: haplotype reconstruction in general pedigrees

this paper allows very rapid multipoint likelihood calculation in nuclear families (with or without parental consanguinity), and the accompanying software package makes multipoint mapping feasible in many experimental contexts. 18 18 Acknowledgments We thank David Botstein and Michele Gschwend for many discussions concerning homozygosity mapping and for sharing unpublished data. We thank Daniel Kastner and his colleagues for sharing the pedigree and genotype data from their FMF studies. We thank Robert Elston, Michael Boehnke, Augustine Kong, and an anonymous referee for comments on the manuscript. This work was supported in part by a grant from the National Institutes of Health (HG00098) to E.S.L. 19 19 Appendix: Description of algorithm Consider a fixed map of M ordered marker loci with known recombination fractions q i between loci i and i+1. We wish to compute the likelihood for a given pedigree. Following Lander and Green (1987), the inheritance pattern at each locus i (i=1, 2, ..., M) can be described by an n-bit vector v i . Each bit describes the outcome of one of the n meioses in the pedigree: the bit is 0 if the paternally derived allele is transmitted and 1 if the maternally derived allele is transmitted. The set of all possible n-bit vectors will be identified with Z 2 ( )

Genetic Analysis Workshop 10 identified five key factors contributing to the resolution of the genetic factors affecting complex traits. These include analysis with multipoint methods, use of extended pedigrees, and selective sampling of pedigrees. By sampling the affected individuals in an extended pedigree, we obtain individuals who have an increased probability of sharing genes identical by descent (IBD) at marker loci that are linked to the trait locus or loci. Given marker data on specified members of a pedigree, the conditional IBD status among relatives can be assessed, but exact computation is often impractical for multiple linked markers on complex pedigrees. The use of Markov chain Monte Carlo (MCMC) methods greatly extends the range of models and data sets for which analysis is computationally feasible. Many forms of MCMC have now been implemented in the context of genetic analysis. Here we propose a new sampler, which takes as latent variables the segregation indicators at marker loci, and jointly updates all indicators corresponding to a given meiosis. The sampler has good mixing properties. Questions of irreducibility are also addressed.

ion in Models The full probabilistic and decision analytic framework for reasoning about uncertainty is very attractive and has a long history of advocacy and analysis (e.g., [17,30]). Nevertheless, applying these ideas in a straightforward manner requires accurate elicitation of many numeric probabilities and utilities. The difficulty of doing this begs for practical or conceptual simplification. Early AIM and AI programs introduced a large variety of scoring schemes that were thought, at the time, to be simpler or more attractive than probability theory. In retrospect, however, many of these have been shown to be equivalent to standard probability theory, with perhaps a few additional assumptions or approximations (e.g., [12] concerning Mycin, and the discussion of log likelihood ratios, above, for Internist). Some of the schemes were originally introduced simply because the methods of Bayes networks were unknown, yet the need for chains of probabilistic inference was critical (e.g...

This paper was published in Cytogenetics and Cell Genetics, Vol. 59, pages 136–138, 1992. Efficient computation of probabilistic relationships over family pedigrees is an important tool for a variety of problems in genetics, including genetic counseling and linkage analysis. The development of faster and more comprehensive algorithms has preoccupied geneticists for decades [?], and recent general-purpose algorithms for probabilistic inference over arbitrary networks (e.g., [?]) have also been proposed as useful tools for such problems [?]. We present a set of engineering speed-up methods developed as part of the implementation of a prototype program for assisting genetic counselors, geninfer-ii. The design of the underlying computational algorithm is due to Cooper [?], and treats the problem of finding an efficient way to evaluate a Bayes network as a problem of factoring algebraic formulæ. It is thus an extension of the method of [?] (though I believe it was independently formulated) and handles consanguinity by extending the factoring method rather than by cutset conditioning (as does, for example, [?]). The main arguments presented in this paper are: 1. It is profitable to treat the formulæ that describe a pedigree and its associated information as