Recent advancement in microarray technologies has led to a collection of an enormous number of genetic markers in disease association studies, and yet scientists are interested in selecting a smaller set of genes to explore the relation between genes and disease. Current approaches either adopt a single marker test which ignores the possible interaction among genes or consider a multistage procedure that reduces the large size of genes before evaluation of the association. Among the latter, Bayesian analysis can further accommodate the correlation between genes through the specification of a multivariate prior distribution and estimate the probabilities of association through latent variables. The covariance matrix, however, depends on an unknown parameter. In this research, we suggested a reference hyperprior distribution for such uncertainty, outlined the implementation of its computation, and illustrated this fully Bayesian approach with a colon and leukemia cancer study. Comparison with other existing methods was also conducted. The classification accuracy of our proposed model is higher with a smaller set of selected genes. The results not only replicated findings in several earlier studies, but also provided the strength of association with posterior probabilities. 1. Introduction Recent advancement in oligonucleotide microarray technologies has resulted in production of thousands of gene expression levels in a single experiment. With such vast amount of data, one major task for researchers is to develop classification rules for prediction of cancers or cancer subtypes based on gene expression levels of tissue samples. The accuracy of such classification rules may be crucial for diagnosis and treatment, since different cancer subtypes may require different target-specific therapies. However, the development of good and efficient classification rules has not been straightforward, either because of the huge number of genes collected from a relatively small number of tissue samples or because of the model complexity associated with the biological mechanism. The identification of a smaller set of relevant genes to characterize different disease classes, therefore, has been a challenging task. Procedures which are efficient in gene selection as well as in classification do play an important role in cancer research. Many approaches have been proposed for classes classification. For example, several analyses identified a subset of classifying genes with -statistics, regression model approach, mixture model, Wilcoxon score test, or the between-within
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