Inference of posterior inclusion probability of QTLs in Bayesian shrinkage analysis

Bayesian shrinkage analysis estimates all QTLs effects simultaneously, which shrinks the effect of "insignificant" QTLs close to zero so that it does not need special model selection. Bayesian shrinkage estimation usually has an excellent performance on multiple QTLs mapping, but it could not give a probabilistic explanation of how often a QTLs is included in the model, also called posterior inclusion probability, which is important to assess the importance of a QTL. In this research, two methods, FitMix and SimMix, are proposed to approximate the posterior probabilities. Under the assumption of mixture distribution of the estimated QTL effect, FitMix and SimMix mathematically and intuitively fit mixture distribution, respectively. The simulation results showed that both methods gave very reasonable estimates for posterior probabilities. We also applied the two methods to map QTLs for the North American Barley Genome Mapping Project data.