Bayesian analysis of mixture models with application to genetic linkage

Abstract

Through an application to genetic linkage analysis, this project describes how the Bayesian approach can be used for the mixture model with an unknown number of components. Genetic linkage analysis based on a complex model can be difficult to manage when a large number of markers loci and/or large pedigrees are involved, due to computation limitations. However, Markov chain Monte Carlo (MCMC) schemes are one alternative, utilizing a reversible jump steps that allow change on the dimension of parameter space. Thus, the MCMC samplers with a different numbers of quantitative trait loci based on complex large pedigrees can be obtained using reversible jump MCMC methodology. The application of the MCMC scheme is illustrated with a case study of genetic linkage to hypercalciuria. This analysis report found strong evidence for linkage of hypercalciuria to calibrated estimates of Bayes factors, the so-called L-Scores. To my knowledge this is the first time that urinary calcium excretion has been clearly linked to a narrow region of the genome. Nevertheless, further study is needed to confirm this finding.