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Ensemble Inference Methods for Models With Noisy and Expensive Likelihoods

Duncan, Andrew B. and Stuart, Andrew M. and Wolfram, Marie-Therese (2021) Ensemble Inference Methods for Models With Noisy and Expensive Likelihoods. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20210412-121307581

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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. Multiscale analysis is used to study the behaviour of interacting particle system algorithms when such rapid fluctuations, which we refer to as noise, pollute the large scale parametric dependence of the parameter-to-data map. Ensemble Kalman methods (which are derivative-free) and Langevin-based methods (which use the derivative of the parameter-to-data map) are compared in this light. The ensemble Kalman methods are shown to behave favourably 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, whilst 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 favourably.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/2104.03384arXivDiscussion Paper
ORCID:
AuthorORCID
Wolfram, Marie-Therese0000-0003-1133-8253
Additional Information:AD is supported by the UKRI Strategic Priorities Fund under the EPSRC Grant EP/T001569/1, particularly the "Digital Twins for Complex Engineering Systems" theme within that grant, and The Alan Turing Institute. MTW is supported by the New Frontier Grant NST-0001 of the Austrian Academy of Sciences. AMS is supported by NSF (award AGS-1835860), NSF (award DMS-1818977) and by the Office of Naval Research (award N00014-17-1-2079). AMS and MTW are also supported by a Royal Society International Exchange Grant.
Funders:
Funding AgencyGrant Number
Engineering and Physical Sciences Research Council (EPSRC)EP/T001569/1
Alan Turing InstituteUNSPECIFIED
Österreichische Akademie der WissenschaftenNST-0001
NSFAGS-1835860
NSFDMS-1818977
Office of Naval Research (ONR)N00014-17-1-2079
Royal SocietyUNSPECIFIED
Subject Keywords:Multiscale Analysis, Ensemble Kalman Sampler, Langevin sampling, Gaussian process regression
Classification Code:AMS subject classifications: 60H30, 35B27, 60G15, 82C80, 65C35, 62F15
Record Number:CaltechAUTHORS:20210412-121307581
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210412-121307581
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:108700
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:13 Apr 2021 21:34
Last Modified:23 Apr 2021 18:28

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