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Ensemble inference methods for models with noisy and expensive likelihoods
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Dunbar, Oliver R. A., Duncan, Andrew, Stuart, Andrew M. and Wolfram, Marie-Therese (2022) Ensemble inference methods for models with noisy and expensive likelihoods. SIAM Journal on Applied Dynamical Systems, 21 (2). pp. 1539-1572. doi:10.1137/21M1410853 ISSN 1536-0040.
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WRAP-ensemble-inference-methods-models-noisy-expensive-likelihoods-Wolfram-2022.pdf - Accepted Version - Requires a PDF viewer. Download (2153Kb) | Preview |
Official URL: https://doi.org/10.1137/21M1410853
Abstract
The increasing availability of data presents an opportunity to calibrate unknown parameters which appear in complex models of phenomena in the biomedical, physical, and social sciences. However, model complexity often leads to parameter-to-data maps which are expensive to evaluate and are only available through noisy approximations. This paper is concerned with the use of interacting particle systems for the solution of the resulting inverse problems for parameters. Of particular interest is the case where the available forward model evaluations are subject to rapid fluctuations, in parameter space, superimposed on the smoothly varying large-scale parametric structure of interest. A motivating example from climate science is presented, and ensemble Kalman methods (which do not use the derivative of the parameter-to-data map) are shown, empirically, to perform well. Multiscale analysis is then used to analyze the behavior of interacting particle system algorithms when rapid fluctuations, which we refer to as noise, pollute the large-scale parametric dependence of the parameter-to-data map. Ensemble Kalman methods and Langevin-based methods (the latter use the derivative of the parameter-to-data map) are compared in this light. The ensemble Kalman methods are shown to behave favorably in the presence of noise in the parameter-to-data map, whereas Langevin methods are adversely affected. On the other hand, Langevin methods have the correct equilibrium distribution in the setting of noise-free forward models, while ensemble Kalman methods only provide an uncontrolled approximation, except in the linear case. Therefore a new class of algorithms, ensemble Gaussian process samplers, which combine the benefits of both ensemble Kalman and Langevin methods, are introduced and shown to perform favorably.
| Item Type: | Journal Article | ||||||
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| Journal or Publication Title: | SIAM Journal on Applied Dynamical Systems | ||||||
| Publisher: | SIAM | ||||||
| ISSN: | 1536-0040 | ||||||
| Official Date: | 21 June 2022 | ||||||
| Dates: |
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| Volume: | 21 | ||||||
| Number: | 2 | ||||||
| Page Range: | pp. 1539-1572 | ||||||
| DOI: | 10.1137/21M1410853 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Reuse Statement (publisher, data, author rights): | First Published in SIAM Journal on Applied Dynamical Systems in 21(2) 2022, published by the Society for Industrial and Applied Mathematics (SIAM) Copyright © by SIAM. Unauthorized reproduction of this article is prohibited | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Date of first compliant deposit: | 21 June 2022 | ||||||
| Date of first compliant Open Access: | 1 July 2022 | ||||||
| Related URLs: | |||||||
| Open Access Version: |
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