Dependent Bayesian multiple hypothesis testing

In modern-day practical statistical problems with many parameters, one is seldom interested in testing only one hypothesis. Simultaneous inference on hundreds of parameters is often necessary, for instance, in spatial, microarray datasets or in analyses of fMRI data. Thus multiple testing has emerged as a very important area in statistical inference and received substantial attention from researchers in both frequentist and Bayesian paradigms. Here we provide a brief overview of multiple testing procedures with particular focus on the Bayesian techniques. In recent times dependent multiple testing has drawn the attention of researchers as often in practical applications the test statistics or parameters of interest have structural dependence. We further discuss a Bayesian nonmarginal multiple testing procedure that uses such dependence structure in the decision procedure for improving accuracy of inference.