Testing-driven Variable Selection in Bayesian Modal Regression
This addresses variable selection for researchers dealing with non-Gaussian errors in fields like genetics, but it appears incremental as it builds on existing Bayesian modal regression frameworks.
The paper tackled variable selection in Bayesian modal regression for heavy-tailed responses by proposing a method that uses a test statistic based on model error distribution shape, and demonstrated its efficacy in simulations and applications to genetic and epigenetic datasets.
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.