A new go-to sampler for Bayesian probit regression

Simmons, Scott; McGuffey, Elizabeth J.; VanDerwerken, Douglas

doi:10.2140/involve.2020.13.77

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A new go-to sampler for Bayesian probit regression

Scott Simmons, Elizabeth J. McGuffey and Douglas VanDerwerken

Vol. 13 (2020), No. 1, 77–89

DOI: 10.2140/involve.2020.13.77

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.

Keywords

probit regression, Markov chain Monte Carlo, Gibbs sampling, Metropolis–Hastings

Mathematical Subject Classification 2010

Primary: 62C10, 62F15

Milestones

Received: 28 January 2019

Accepted: 14 November 2019

Published: 4 February 2020

Communicated by Jem Noelle Corcoran

Authors

Scott Simmons
US Naval Academy Annapolis, MD United States

Elizabeth J. McGuffey
US Naval Academy Annapolis, MD United States

Douglas VanDerwerken
US Naval Academy Annapolis, MD United States

Vol. 13, No. 1, 2020