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Calibrate, Emulate, Sample

Cleary, Emmet and Garbuno-Inigo, Alfredo and Lan, Shiwei and Schneider, Tapio and Stuart, Andrew M. (2020) Calibrate, Emulate, Sample. . (Unpublished)

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Many parameter estimation problems arising in applications are best cast in the framework of Bayesian inversion. This allows not only for an estimate of the parameters, but also for the quantification of uncertainties in the estimates. Often in such problems the parameter-to-data map is very expensive to evaluate, and computing derivatives of the map, or derivative-adjoints, may not be feasible. Additionally, in many applications only noisy evaluations of the map may be available. We propose an approach to Bayesian inversion in such settings that builds on the derivative-free optimization capabilities of ensemble Kalman inversion methods. The overarching approach is to first use ensemble Kalman sampling (EKS) to calibrate the unknown parameters to fit the data; second, to use the output of the EKS to emulate the parameter-to-data map; third, to sample from an approximate Bayesian posterior distribution in which the parameter-to-data map is replaced by its emulator. This results in a principled approach to approximate Bayesian inference that requires only a small number of evaluations of the (possibly noisy approximation of the) parameter-to-data map. It does not require derivatives of this map, but instead leverages the documented power of ensemble Kalman methods. Furthermore, the EKS has the desirable property that it evolves the parameter ensembles towards the regions in which the bulk of the parameter posterior mass is located, thereby locating them well for the emulation phase of the methodology. In essence, the EKS methodology provides a cheap solution to the design problem of where to place points in parameter space to efficiently train an emulator of the parameter-to-data map for the purposes of Bayesian inversion.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper
Garbuno-Inigo, Alfredo0000-0003-3279-619X
Lan, Shiwei0000-0002-9167-3715
Schneider, Tapio0000-0001-5687-2287
Additional Information:All authors are supported by the generosity of Eric and Wendy Schmidt by recommendation of the Schmidt Futures program, by Earthrise Alliance, Mountain Philanthropies, the Paul G. Allen Family Foundation, and the National Science Foundation (NSF, award AGS1835860). A.M.S. is also supported by NSF (award DMS-1818977) and by the Office of Naval Research (award N00014-17-1-2079).
Funding AgencyGrant Number
Schmidt Futures ProgramUNSPECIFIED
EarthRise AllianceUNSPECIFIED
Mountain PhilanthropiesUNSPECIFIED
Paul G. Allen Family FoundationUNSPECIFIED
Office of Naval Research (ONR)N00014-17-1-2079
Subject Keywords:Approximate Bayesian inversion; uncertainty quantification; Ensemble Kalman sampling; Gaussian process emulation; experimental design
Record Number:CaltechAUTHORS:20200402-140348174
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:102274
Deposited By: Tony Diaz
Deposited On:02 Apr 2020 21:12
Last Modified:02 Apr 2020 21:12

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