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

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

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 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.

Suggested Citation

  • Raices Cruz, Ivette & Lindström, Johan & Troffaes, Matthias C.M. & Sahlin, Ullrika, 2022. "Iterative importance sampling with Markov chain Monte Carlo sampling in robust Bayesian analysis," Computational Statistics & Data Analysis, Elsevier, vol. 176(C).
    • Handle: RePEc:eee:csdana:v:176:y:2022:i:c:s0167947322001384
    DOI: 10.1016/j.csda.2022.107558
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    References listed on IDEAS

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    1. Liesenfeld, Roman & Richard, Jean-François, 2008. "Improving MCMC, using efficient importance sampling," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 272-288, December.
    2. John Paul Gosling, 2018. "SHELF: The Sheffield Elicitation Framework," International Series in Operations Research & Management Science, in: Luis C. Dias & Alec Morton & John Quigley (ed.), Elicitation, chapter 0, pages 61-93, Springer.
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    4. Bhattacharya, Sourabh, 2008. "Consistent estimation of the accuracy of importance sampling using regenerative simulation," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2522-2527, October.
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    2. Andral, Charly & Douc, Randal & Marival, Hugo & Robert, Christian P., 2024. "The importance Markov chain," Stochastic Processes and their Applications, Elsevier, vol. 171(C).

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