Iterative importance sampling with Markov chain Monte Carlo sampling in robust Bayesian analysis

Raices Cruz, Ivette; Lindström, Johan; Troffaes, Matthias C.M.; Sahlin, Ullrika

doi:10.1016/j.csda.2022.107558

Iterative importance sampling with Markov chain Monte Carlo sampling in robust Bayesian analysis

Raices Cruz, Ivette; Lindström, Johan; Troffaes, Matthias C.M.; Sahlin, Ullrika

Authors

Ivette Raices Cruz

Johan Lindström

Professor Matthias Troffaes matthias.troffaes@durham.ac.uk
Professor

Ullrika Sahlin

Abstract

Bayesian inference under a set of priors, called robust Bayesian analysis, allows for estimation of parameters within a model and quantification of epistemic uncertainty in quantities of interest by bounded (or imprecise) probability. Iterative importance sampling can be used to estimate bounds on the quantity of interest by optimizing over the set of priors. A method for iterative importance sampling when the robust Bayesian inference rely on Markov chain Monte Carlo (MCMC) sampling is proposed. To accommodate the MCMC sampling in iterative importance sampling, a new expression for the effective sample size of the importance sampling is derived, which accounts for the correlation in the MCMC samples. To illustrate the proposed method for robust Bayesian analysis, iterative importance sampling with MCMC sampling is applied to estimate the lower bound of the overall effect in a previously published meta-analysis with a random effects model. The performance of the method compared to a grid search method and under different degrees of prior-data conflict is also explored.

Citation

Raices Cruz, I., Lindström, J., Troffaes, M. C., & Sahlin, U. (2022). Iterative importance sampling with Markov chain Monte Carlo sampling in robust Bayesian analysis. Computational Statistics & Data Analysis, 176, Article 107558. https://doi.org/10.1016/j.csda.2022.107558

Journal Article Type	Article
Acceptance Date	Jun 23, 2022
Online Publication Date	Jul 13, 2022
Publication Date	2022-12
Deposit Date	Jun 16, 2022
Publicly Available Date	Jul 14, 2022
Journal	Computational Statistics & Data Analysis
Print ISSN	0167-9473
Publisher	Elsevier
Peer Reviewed	Peer Reviewed
Volume	176
Article Number	107558
DOI	https://doi.org/10.1016/j.csda.2022.107558
Related Public URLs	https://arxiv.org/abs/2206.08728

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http://creativecommons.org/licenses/by/4.0/

Copyright Statement
© 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/).