Importance sampling methods for Bayesian discrimination between embedded models

Marin, Jean-Michel; Robert, Christian P.

Marin, Jean-Michel; Robert, Christian P. (2010), Importance sampling methods for Bayesian discrimination between embedded models, in Chen, M.H.; Müller, P.; Sun, D.; Ye, K.; Dey, D., Frontiers of Statistical Decision Making and Bayesian Analysis, Springer : Berlin Heidelberg, p. 513-527. 10.1007/978-1-4419-6944-6_14

Type

Chapitre d'ouvrage

External document link

https://hal.archives-ouvertes.fr/hal-00424475

Date

2010

Book title

Frontiers of Statistical Decision Making and Bayesian Analysis

Book author

Chen, M.H.; Müller, P.; Sun, D.; Ye, K.; Dey, D.

Publisher

Springer

Published in

Berlin Heidelberg

ISBN

978-1-4419-6943-9

Pages

513-527

Abstract (EN)

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.

Subjects / Keywords

importance sampling; bridge sampling; harmonic mean; Chib's estimator; Bayesian model choice