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In this work, we characterize genes using an oligonucleotide affymetrix gene expression dataset and propose a novel gene selection method based on samples from the posterior distributions of class-specific gene expression measures. We construct a hierarchical Bayesian framework for a random effect ANOVA model that allows us to obtain the posterior distributions of the class-specific gene expressions. We also formalize a novel class prediction scheme based on the samples from new posterior distributions of group specific gene expressions. Our experimental results show the class-discriminating power of the selected genes. Furthermore, we demonstrate that our prediction scheme classifies tissue samples into appropriate treatment groups with high accuracy. The computations are implemented by using Gibbs sampling. We compare the efficacy of our proposed gene selection and prediction methods with that of Pomeroy et. al (Nature, 2002) on the same CNS tumor sample dataset.