Bayesian analysis of comparative microarray experiments by model averaging

Abstract

A major challenge to the statistical analysis of microarray data is the small number of samples — limited by both cost and sample availability — compared to the large number of genes, now soaring into the tens of thousands per experiment. This situation is made even more difficult by the complex nature of the empirical distributions of gene expression measurements and the necessity to limit the number of false detections due to multiple comparisons. This paper introduces a novel Bayesian method for the analysis of comparative experiments performed with oligonucleotide microarrays. Our method models gene expression data by log-normal and gamma distributions with hierarchical prior distributions on the parameters of interest, and uses model averaging to compute the posterior probability of differential expression. An initial approximate Bayesian analysis is used to identify genes that have a large probability of differential expression, and this list of candidate genes is further refined by using stochastic computations. We assess the performance of this method using real data sets and show that it has an almost negligible false positive rate in small sample experiments that leads to a better detection performance.