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Approximate Bayesian computation with the Wasserstein distance
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Bernton, Espen, Jacob, Pierre, Gerber, Mathieu and Robert, Christian P. (2019) Approximate Bayesian computation with the Wasserstein distance. Journal of the Royal Statistical Society Series B: Statistical Methodology, 81 (2). pp. 235-269. doi:10.1111/rssb.12312 ISSN 1369-7412.
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Official URL: https://doi.org/10.1111/rssb.12312
Abstract
A growing number of generative statistical models do not permit the numerical evaluation of their likelihood functions. Approximate Bayesian computation has become a popular approach to overcome this issue, in which one simulates synthetic data sets given parameters and compares summaries of these data sets with the corresponding observed values. We propose to avoid the use of summaries and the ensuing loss of information by instead using the Wasserstein distance between the empirical distributions of the observed and synthetic data. This generalizes the well‐known approach of using order statistics within approximate Bayesian computation to arbitrary dimensions. We describe how recently developed approximations of the Wasserstein distance allow the method to scale to realistic data sizes, and we propose a new distance based on the Hilbert space filling curve. We provide a theoretical study of the method proposed, describing consistency as the threshold goes to 0 while the observations are kept fixed, and concentration properties as the number of observations grows. Various extensions to time series data are discussed. The approach is illustrated on various examples, including univariate and multivariate g‐and‐k distributions, a toggle switch model from systems biology, a queuing model and a Lévy‐driven stochastic volatility model.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||
| Library of Congress Subject Headings (LCSH): | Bayesian statistical decision theory | ||||||||
| 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 2019 | ||||||||
| Dates: |
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| Volume: | 81 | ||||||||
| Number: | 2 | ||||||||
| Page Range: | pp. 235-269 | ||||||||
| DOI: | 10.1111/rssb.12312 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Reuse Statement (publisher, data, author rights): | "This is the peer reviewed version of the following article:Bernton, E. , Jacob, P. E., Gerber, M. and Robert, C. P. (2019), Approximate Bayesian computation with the Wasserstein distance. J. R. Stat. Soc. B. which has been published in final form at doi:10.1111/rssb.12312. 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 | ||||||||
| Copyright Holders: | John Wiley | ||||||||
| Date of first compliant deposit: | 14 March 2019 | ||||||||
| Date of first compliant Open Access: | 17 February 2020 | ||||||||
| RIOXX Funder/Project Grant: |
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| Open Access Version: |
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