Empirical and fully Bayesian approaches for random effects models in microarray data analysis

A linear model involving a mixture distribution is considered for the comparison of normalized microarray data from two treatment groups. Model fitting using an empirical Bayes approach has been shown to be both accurate and numerically stable. The posterior odds of treatment/gene interactions derived from the model involve shrinkage estimates of both the interactions and the gene-specific error variances, leading to powerful inference. We show that the same model can easily be fit under a fully Bayesian framework, allowing increased flexibility in terms of prior distributional assumptions and posterior inference.