The analysis of the high-dimensional data generated by DNA microarrays poses challenge to standard statistical methods. In this talk I will describe how Bayesian methodologies for variable selection can be successfully employed in the analysis of
genomics data. In particular I will describe how mixture priors and stochastic search techniques, originally developed for variable selection in regression settings, can be successfully adapted to a variety of different problems, including methods for sample classification and clustering, and to survival models. I will describe the key ideas of these statistical methods and will present applications to data from microarray studies. The proposed methods will allow the identification of genes that discriminate the samples into distinct subclasses. Molecular classes defined on a small number of genes can lead to a better understanding of the underlying biological processes. In addition, the selected genes can serve as biomarkers for improved diagnosis and targets for therapeutic intervention.