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Model misspecification in approximate Bayesian computation : consequences and diagnostics
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Frazier, David T., Robert, Christian P. and Rousseau, Judith (2020) Model misspecification in approximate Bayesian computation : consequences and diagnostics. Journal of the Royal Statistical Society Series B: Statistical Methodology, 82 (2). pp. 421-444. doi:10.1111/rssb.12356 ISSN 1369-7412.
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Official URL: https://doi.org/10.1111/rssb.12356
Abstract
We analyze the behavior of approximate Bayesian computation (ABC) when the model generating the simulated data differs from the actual data generating process; i.e., when the data simulator in ABC is misspecified. We demonstrate both theoretically and in simple, but practically relevant, examples that when the model is misspecified different versions of ABC can yield substantially different results. Our theoretical results demonstrate that even though the model is misspecified, under regularity conditions, the accept/reject ABC approach concentrates posterior mass on an appropriately defined pseudo-true parameter value. However, under model misspecification the ABC posterior does not yield credible sets with valid frequentist coverage and has non-standard asymptotic behavior. In addition, we examine the theoretical behavior of the popular local regression adjustment to ABC under model misspecification and demonstrate that this approach concentrates posterior mass on a completely different pseudo-true value than accept/reject ABC. Using our theoretical results, we suggest two approaches to diagnose model misspecification in ABC. All theoretical results and diagnostics are illustrated in a simple running example.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > Q Science (General) Q Science > QA Mathematics |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||
| Journal or Publication Title: | Journal of the Royal Statistical Society Series B: Statistical Methodology | ||||||||
| Publisher: | Wiley-Blackwell Publishing, Inc | ||||||||
| ISSN: | 1369-7412 | ||||||||
| Official Date: | April 2020 | ||||||||
| Dates: |
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| Volume: | 82 | ||||||||
| Number: | 2 | ||||||||
| Page Range: | pp. 421-444 | ||||||||
| DOI: | 10.1111/rssb.12356 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Reuse Statement (publisher, data, author rights): | "This is the peer reviewed version of the following article: Frazier, D.T., Robert, C.P. and Rousseau, J. (2020), Model misspecification in approximate Bayesian computation: consequences and diagnostics. J. R. Stat. Soc. B., which has been published in final form at https://doi.org/10.1111/rssb.12356. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions." | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Date of first compliant deposit: | 27 November 2019 | ||||||||
| Date of first compliant Open Access: | 8 January 2021 | ||||||||
| Funder: | Institut Universitaire de France | ||||||||
| Related URLs: | |||||||||
| Open Access Version: |
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