Use of mixture models in multiple hypothesis testing with applications in bioinformatics

There are many important problems these days where consideration has to be given to carrying out hundreds or even thousands of hypothesis testing problems at the same time. For example, in forming classifiers on the basis of high-dimensional data, the aim might be to select a small subset of useful variables for the prediction problem at hand. In the field of bioinformatics, there are many examples where a large number of hypotheses have to be tested simultaneously. For example, a common problem is the detection of genes that are differentially expressed in a given number of classes. The problem of testing many hypotheses at the same time can be expressed in a two-component mixture framework, using an empirical Bayes approach; see, for example, Efron (2004). In this framework, we present further results as part of an ongoing investigation into the approach of McLachlan et al. (2006) on the adoption of normal mixture models to provide a parametric approach to the estimation of the so-called local false discovery rate. The latter can be viewed as the posterior probability that a given null hypothesis does hold. With this approach, not only can the global false discovery rate be controlled, but also the implied probability of a false negative can be assessed. The methodology is demonstrated on some problems in bioinformatics