The Bayesian t-Test and Beyond

In this chapter we will explore Bayesian alternatives to the t -test. We saw in Chapter 1 how t -test can be used to test whether the expected outcomes of the two groups are equal or not. In Chapter 3 we saw how to make inferences from a Bayesian perspective in principle. In this chapter we will put these together to develop a Bayesian procedure for a t -test. This procedure depends on the data only through the t -statistic. It requires prior inputs and we will discuss how to assign them. We will use an example from a microarray study as to demonstrate the practical issues. The microarray study is an important application for the Bayesian t -test as it naturally brings up the question of simultaneous t -tests. It turns out that the Bayesian procedure can easily be extended to carry several t -tests on the same data set, provided some attention is paid to the concept of the correlation between tests.