Fast Bayesian variable screenings for binary response regressions with small sample size

ABSTRACT

Screening procedures play an important role in data analysis, especially in high-throughput biological studies where the datasets consist of more covariates than independent subjects. In this article, a Bayesian screening procedure is introduced for the binary response models with logit and probit links. In contrast to many screening rules based on marginal information involving one or a few covariates, the proposed Bayesian procedure simultaneously models all covariates and uses closed-form screening statistics. Specifically, we use the posterior means of the regression coefficients as screening statistics; by imposing a generalized g-prior on the regression coefficients, we derive the analytical form of their posterior means and compute the screening statistics without Markov chain Monte Carlo implementation. We evaluate the utility of the proposed Bayesian screening method using simulations and real data analysis. When the sample size is small, the simulation results suggest improved performance with comparable computational cost.

KEYWORDS:

• g-prior
• logistic regression
• probit regression
• sure independence screening

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Chang's research was partially supported by Ministry of Science and Technology (MOST) of Taiwan under [grant no. 103-2118-M-006-004-]. Tzeng's research was supported by NIH [grant no. P01 CA142538]. Chen's research was partially supported by Ministry of Science and Technology (MOST) of Taiwan [grant no. 103-2118-M-006-002-MY2] and the Mathematics Division of the National Center for Theoretical Sciences in Taiwan.