A new go-to sampler for Bayesian probit regression

Abstract

This paper introduces an independent-proposal Metropolis–Hastings sampler for Bayesian probit regression. The Gibbs sampler of Albert and Chib has been the default sampler since its introduction in 1993. We conduct a simulation study comparing the two methods under various combinations of predictor variables and sample sizes. The proposed sampler is shown to outperform that of Albert and Chib in terms of efficiency measured through autocorrelation, effective sample size, and computation time. We then demonstrate performance of the samplers on real data applications with analogous results.