A bayesian approach to map QTLs using reversible jump MCMC

The use of Bayesian methodology in genetic applications has grown increasingly popular, in particular in the analysis of quantitative trait loci (QTL) for studies using molecular markers. In such analyses the objectives are mapping QTLs, estimating their locations in the genome and their genotypic effects (additive, dominance, and epistatic). The Bayesian approach proceeds by setting up a likelihood function for the phenotype and assigning prior distributions to all unknown quantities in the model (number, chromosome, locus, and genetic effects of QTL). These induce a posterior distribution of the unknown quantities that contains all of the available information for inference of the genetic architecture of the trait. Bayesian mapping methods can treat the unknown number of QTL as a random variable, which has several advantages but results in the complication of varying the dimension of the model space. The reversible jump MCMC algorithm (MCMC-RJ), proposed by Green (1995), offers a powerful and general approach to exploring posterior distributions in this setting. The method was evaluated by analyzing simulated data in WinQTLCart, attributing different priors distributions on the QTL numbers.