Bayesian Variable Screenings for Binary Response Regressions in High-Dimensional and Sparse Settings

Abstract

Screening procedures have become a widely used part of modern statistical analysis, especially when datasets consist of more covariates than independent subjects. Current screening approaches for binary response models either rely on marginal effects or suffer from the nonexistence of maximum likelihood estimates when a joint screening is performed. Bayesian screening procedures can avoid the nonexistence issue; however, these procedures impose enormous computational burdens due to the evaluation of high-dimensional integrals or Markov chain Monte Carlo iterations. In this article, we derive Bayesian screening methods with closed-form screening statistics for binary responses based on probit and logit links, avoiding the Markov chain Monte Carlo step. In these methods, we jointly consider all of the covariates in one model, and the screening statistics are the posterior means of regression coefficients. Given the proposed generalized g-prior for regression coefficients, the closed-form posterior means are derived directly; their uniqueness are also guaranteed. Simulation studies have demonstrated that the proposed Bayesian screening procedures have comparable or better performance than the benchmark method, which is iterative sure independence screening Fan and Song (2010). Finally, a real example related to the discrimination of leukemia types is used to illustrate the usefulness of the proposed method.