When using a frequentist approach to control the type I error or the family wise error rates in multiple testing, one can increase the power only by increasing the sample size. This is not the case with Bayesian procedures. Bayesian hypothesis testing does not base the decision to reject the null hypothesis on the significance level and every hypothesis is tested independently from the others. However, the threshold used on the posterior probability of the hypotheses implies that every time a null hypothesis is rejected because the posterior probability of the null hypothesis P(H0) is smaller than a chosen threshold, there is a probability P(H0) of error. One can use this number to compute the probability of one or more errors, and assess the global error rates through simulations. Figure 4 shows examples of different Bayesian decision rules to genome-wide hypothesis testing and their sensitivity and specificity in a small sample study. The prior probability of the hypotheses can also incorporate information about the number of hypotheses that are expected to be true [93,94].
