# Bayesian Methods Applied to GWAS

Bayesian multiple-regression methods are being successfully used for genomic prediction and selection. These regression models simultaneously fit many more markers than the number of observations available for the analysis. Thus, the Bayes theorem is used to combine prior beliefs of marker effects, which are expressed in terms of prior distributions, with information from data for inference. Often, the analyses are too complex for closed-form solutions and Markov chain Monte Carlo (MCMC) sampling is used to draw inferences from posterior distributions. This chapter describes how these Bayesian multiple-regression analyses can be used for GWAS. In most GWAS, false positives are controlled by limiting the genome-wise error rate, which is the probability of one or more false-positive results, to a small value. As the number of test in GWAS is very large, this results in very low power. Here we show how in Bayesian GWAS false positives can be controlled by limiting the proportion of false-positive results among all positives to some small value. The advantage of this approach is that the power of detecting associations is not inversely related to the number of markers.

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