Work

Empirical Bayes inference in sparse high-dimensional generalized linear models

Year: 2024

Type: article

Abstract: High-dimensional linear models have been widely studied, but the developments in high-dimensional generalized linear models, or GLMs, have been slower. In this paper, we propose an empirical or data-driven prior leading to an empirical Bayes posterior distribution which can be used for estimation of and inference on the coefficient vector in a high-dimensional GLM, as well as for variable selection. We prove that our proposed posterior concentrates around the true/sparse coefficient vector at the optimal rate, provide conditions under which the posterior can achieve variable selection consistency, and prove a Bernstein–von Mises theorem that implies asymptotically valid uncertainty quantification. Computation of the proposed empirical Bayes posterior is simple and efficient, and is shown to perform well in simulations compared to existing Bayesian and non-Bayesian methods in terms of estimation and variable selection.

Source: Electronic Journal of Statistics

DOI: 10.1214/24-ejs2274

Authors: Yiqi Tang, Ryan Martin

Institutions: Colby College, North Carolina State University

Language: English

Topic: Statistical Methods and Inference

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $675

Funder: National Science Foundation