Probabilistic Inference in Modern Genetic Linkage Analysis

Abstract

Exact inference can be computationally intractable. When it is infeasible or impractical, one often resorts to approximate methods. This thesis focuses on the algorithms for approximate inference and their applications in modern genetic linkage analysis. The first part of the thesis concentrates on an application of inference algorithms in modern genetic linkage analysis. We develop a computationally efficient method for multipoint linkage analysis on extended pedigrees for trait models having a two-locus Quantitative Trait Locus (QTL) effect. The method is implemented in the program, hg_lod, which uses Markov Chain Monte Carlo (MCMC) method to sample realizations of descent patterns conditional on marker data, then calculates the trait likelihoods by an efficient exact probabilistic inference algorithm. hg_lod can handle data on large pedigrees with a lot of unobserved individuals, and can compute accurate estimates of lod scores at a much larger number of hypothesized locations than can any existing method. In the second part of this thesis, we focus on the theory of general probabilistic inference algorithms. We propose a convex relaxation method as an approximate inference algorithm. We give a convergence analysis of this method by deriving sufficient conditions for its convergence from a mathematical programming point of view. We then show that this method is amenable to coarse-grained parallelization and propose techniques to parallelize it optimally without sacrificing convergence.