Empirical Bayesian QTL Mapping

Abstract

Empirical Bayesian is still a Bayesian method, but thehyperparameters (the parameters of the prior distribution) are not preselected by the investigators; instead, they are estimated from the same dataset as that used in the Bayesian analysis. Once the hyperparameters are estimated, they are used in the usual Bayesian analysis as if they were the true hyperparameters of the prior distributions. The data are actually used twice, once for estimating the hyperparameters and once for estimating the Bayesian posterior means of the parameters of interest. In QTL mapping, the parameters of interest are the QTL effects. A normal prior distribution is assigned to each QTL effect. The variance in the normal prior is a hyperparameter. In the Bayesian shrinkage analysis described earlier, the variance is assigned a higher level of prior distribution so that a posterior distribution of the variance parameter can be derived and the variance is then sampled via the MCMC sampling algorithm. The posterior distribution of the variance depends on the QTL effect. In the empirical Bayesian analysis, we estimate the prior variance before the Bayesian analysis.