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

Raices Cruz, Ivette LU ; Lindström, Johan LU orcid ; Troffaes, Matthias C.M. and Sahlin, Ullrika LU orcid (2022) In Computational Statistics and Data Analysis 176.
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 relies 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... (More)

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 relies 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.

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author
; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Bounds on probability, Effective sample size, Meta-analysis, Random effects model, Uncertainty quantification
in
Computational Statistics and Data Analysis
volume
176
article number
107558
publisher
Elsevier
external identifiers
  • scopus:85134321644
ISSN
0167-9473
DOI
10.1016/j.csda.2022.107558
language
English
LU publication?
yes
additional info
Publisher Copyright: © 2022 The Author(s)
id
3ffca7eb-d526-4a34-b630-61b0c0e51061
date added to LUP
2022-09-05 13:57:53
date last changed
2025-04-04 14:57:33
@article{3ffca7eb-d526-4a34-b630-61b0c0e51061,
  abstract     = {{<p>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 relies 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.</p>}},
  author       = {{Raices Cruz, Ivette and Lindström, Johan and Troffaes, Matthias C.M. and Sahlin, Ullrika}},
  issn         = {{0167-9473}},
  keywords     = {{Bounds on probability; Effective sample size; Meta-analysis; Random effects model; Uncertainty quantification}},
  language     = {{eng}},
  publisher    = {{Elsevier}},
  series       = {{Computational Statistics and Data Analysis}},
  title        = {{Iterative importance sampling with Markov chain Monte Carlo sampling in robust Bayesian analysis}},
  url          = {{http://dx.doi.org/10.1016/j.csda.2022.107558}},
  doi          = {{10.1016/j.csda.2022.107558}},
  volume       = {{176}},
  year         = {{2022}},
}