Importance sampling methods for Bayesian discrimination between embedded models

TL;DR

This paper reviews importance sampling techniques for Bayesian model comparison, highlighting their implementation for testing predictor significance in probit models and comparing their effectiveness on real data.

Contribution

It provides a comprehensive survey of importance sampling methods for Bayesian discrimination, including practical implementation and performance comparison.

Findings

Importance sampling methods vary in efficiency for Bayesian model choice.

Chib's method offers a functional equality exploitation advantage.

Performance differences are demonstrated on a real dataset.

Abstract

This paper surveys some well-established approaches on the approximation of Bayes factors used in Bayesian model choice, mostly as covered in Chen et al. (2000). Our focus here is on methods that are based on importance sampling strategies rather than variable dimension techniques like reversible jump MCMC, including: crude Monte Carlo, maximum likelihood based importance sampling, bridge and harmonic mean sampling, as well as Chib's method based on the exploitation of a functional equality. We demonstrate in this survey how these different methods can be efficiently implemented for testing the significance of a predictive variable in a probit model. Finally, we compare their performances on a real dataset.