Estimating the evidence -- a review

TL;DR

This paper reviews various methods for estimating model evidence in Bayesian statistics, providing guidelines and practical advice, and compares these methods through examples involving Gaussian linear regression and logistic regression.

Contribution

It offers a comprehensive review of evidence estimation methods, including practical guidelines and a comparative analysis using real examples.

Findings

Different evidence estimation methods are compared in practical scenarios.

Guidelines are provided for choosing appropriate evidence estimation techniques.

The review aids practitioners in selecting suitable methods for Bayesian model comparison.

Abstract

The model evidence is a vital quantity in the comparison of statistical models under the Bayesian paradigm. This paper presents a review of commonly used methods. We outline some guidelines and offer some practical advice. The reviewed methods are compared for two examples; non-nested Gaussian linear regression and covariate subset selection in logistic regression.