Multiple hypothesis testing: a Bayesian approach

Recently, the field of multiple hypothesis testing has experimented a great expansion, basically because of the new methods developed in the field of genomics. This new methods allows the scientists to process simultaneously thousands of null hypothesis. The frequentist approach to this problem is made by using different testing error measures that allow to control the Type I error rate at a certain desired level. In this paper, a parametric Bayesian analysis is developed to produced a list of rejected hypothesis which will be declared significant (interesting) for a more detailed analysis. The results are compared with the frequentist False Discovery Rate (FDR) methodology. Simulation examples show the differences between both approaches.