Vol. 13, No. 1, 2020

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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

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.

probit regression, Markov chain Monte Carlo, Gibbs sampling, Metropolis–Hastings
Mathematical Subject Classification 2010
Primary: 62C10, 62F15
Received: 28 January 2019
Accepted: 14 November 2019
Published: 4 February 2020

Communicated by Jem Noelle Corcoran
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