An Algorithm for Bayesian Variable Selection in High-dimensional Generalized Linear Models

Inspired by analysis of genomic data, the primary quest is to identify associations between studied traits and genetic markers where number of markers is typically much larger than sample size. Bayesian variable selection methods with Markov chain Monte Carlo (MCMC) are extensively applied to analyze such high-dimensional data. However, MCMC is often slow to converge with large number of candidate predictors. In this study, we examine the empirical Bayes variable selection with a sparse prior on the unknown coefficients. An iterated conditional modes/medians (ICM/M) algorithm is proposed for implementation by iteratively minimizing a conditional loss function in high-dimensional linear regression model. Attention is then directed to extend the algorithm to a generalized linear model. The performances of our approach are evaluated through simulation study