Testing-driven Variable Selection in Bayesian Modal Regression

TL;DR

This paper introduces a Bayesian variable selection approach tailored for modal regression with heavy-tailed responses, utilizing an EM algorithm and a novel test statistic to identify important covariates effectively.

Contribution

It presents a new Bayesian variable selection method with an efficient EM algorithm and a test statistic based on error distribution shape for modal regression.

Findings

Effective in identifying important covariates with non-Gaussian errors

Demonstrated through simulations and real genetic/epigenetic data

Outperforms existing methods in heavy-tailed response scenarios

Abstract

We propose a Bayesian variable selection method in the framework of modal regression for heavy-tailed responses. An efficient expectation-maximization algorithm is employed to expedite parameter estimation. A test statistic is constructed to exploit the shape of the model error distribution to effectively separate informative covariates from unimportant ones. Through simulations, we demonstrate and evaluate the efficacy of the proposed method in identifying important covariates in the presence of non-Gaussian model errors. Finally, we apply the proposed method to analyze two datasets arising in genetic and epigenetic studies.