A Bayesian Mixture Model for Differential Gene Expression

We propose model-based inference for differential gene expression, using a non-parametric Bayesian probability model for the distribution of gene intensities under different conditions. The probability model is essentially a mixture of normals. The resulting inference is similar to the empirical Bayes approach proposed in Efron et al. (2001). The use of fully modelbased inference mitigates some of the necessary limitations of the empirical Bayes method. However, the increased generality of our method comes at a price. Computation is not as straightforward as in the empirical Bayes scheme. But we argue that inference is no more difficult than posterior simulation in traditional nonparametric mixture of normal models. We illustrate the proposed method in two examples, including a simulation study and a microarray experiment to screen for genes with differential expression in colon cancer versus normal tissue (Alon et al., 1999).