A new Monte Carlo sampling in Bayesian probit regression

TL;DR

This paper introduces a new Monte Carlo sampling method for Bayesian probit regression with uniform and Gaussian priors, offering a potentially more efficient alternative to MCMC for posterior simulation.

Contribution

It presents an alternative posterior form enabling simple Monte Carlo sampling for Bayesian probit regression, improving computational efficiency over traditional MCMC methods.

Findings

New Monte Carlo sampling method for Bayesian probit regression

Explicit expressions for posterior moments with uniform and Gaussian priors

Potential computational efficiency gains over MCMC

Abstract

We study probit regression from a Bayesian perspective and give an alternative form for the posterior distribution when the prior distribution for the regression parameters is the uniform distribution. This new form allows simple Monte Carlo simulation of the posterior as opposed to MCMC simulation studied in much of the literature and may therefore be more efficient computationally. We also provide alternative explicit expression for the first and second moments. Additionally we provide analogous results for Gaussian priors.