Bayesian variable selection with sparse and correlation priors for high-dimensional data analysis

The main challenge in working with gene expression microarrays is that the sample size is small compared to the large number of variables (genes). In many studies, the main focus is on finding a small subset of the genes, which are the most important ones for differentiating between different types of cancer, for simpler and cheaper diagnostic arrays. In this paper, a sparse Bayesian variable selection method in probit model is proposed for gene selection and classification. We assign a sparse prior for regression parameters and perform variable selection by indexing the covariates of the model with a binary vector. The correlation prior for the binary vector assigned in this paper is able to distinguish models with the same size. The performance of the proposed method is demonstrated with one simulated data and two well known real data sets, and the results show that our method is comparable with other existing methods in variable selection and classification.