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Sequential Monte Carlo methods for Bayesian elliptic inverse problems

Beskos, Alexandros and Jasra, Ajay and Muzaffer, Ege A. and Stuart, Andrew M. (2015) Sequential Monte Carlo methods for Bayesian elliptic inverse problems. Statistics and Computing, 25 (4). pp. 727-737. ISSN 1573-1375.

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In this article, we consider a Bayesian inverse problem associated to elliptic partial differential equations in two and three dimensions. This class of inverse problems is important in applications such as hydrology, but the complexity of the link function between unknown field and measurements can make it difficult to draw inference from the associated posterior. We prove that for this inverse problem a basic sequential Monte Carlo (SMC) method has a Monte Carlo rate of convergence with constants which are independent of the dimension of the discretization of the problem; indeed convergence of the SMC method is established in a function space setting. We also develop an enhancement of the SMC methods for inverse problems which were introduced in Kantas et al. (SIAM/ASA J Uncertain Quantif 2:464–489, 2014); the enhancement is designed to deal with the additional complexity of this elliptic inverse problem. The efficacy of the methodology and its desirable theoretical properties, are demonstrated for numerical examples in both two and three dimensions.

Item Type:Article
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Additional Information:© 2015 Springer. Accepted: 8 March 2015.
Subject Keywords:Inverse problems, Elliptic PDEs, Groundwater flow, Adaptive SMC, Markov chain Monte Carlo
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Other Numbering System NameOther Numbering System ID
Andrew StuartJ117
Issue or Number:4
Record Number:CaltechAUTHORS:20160715-172126693
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Official Citation:Beskos, A., Jasra, A., Muzaffer, E.A. et al. Stat Comput (2015) 25: 727. doi:10.1007/s11222-015-9556-7
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:69077
Deposited By: Linda Taddeo
Deposited On:18 Jul 2016 18:52
Last Modified:03 Oct 2019 10:18

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