In this article, we consider the problem of simultaneous testing of hypotheses when the individual test statistics are not necessarily independent. Specifically, we consider the problem of simultaneous testing of point null hypotheses against two-sided alternatives about the mean parameters of normally distributed random variables. We assume that conditionally given the vector means, these random variables jointly follow a multivariate normal distribution with a known but arbitrary covariance matrix. We consider a Bayesian framework where each unknown mean parameter is modeled through a two-component point mass mixture prior, whereby unconditionally the test statistics jointly have a mixture of multivariate normal distributions. A new testing procedure is developed that uses the dependence among the test statistics and works in a step down like manner. This procedure is general enough to be applied to even for non-normal data. A decision theoretic justification in favor of the proposed 查看全文>>