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Sequential Monte Carlo methods for Bayesian elliptic inverse problems

Beskos, A; Jasra, A; Muzaffer, EA; Stuart, AM; (2015) Sequential Monte Carlo methods for Bayesian elliptic inverse problems. Statistics and Computing , 25 (4) pp. 727-737. 10.1007/s11222-015-9556-7. Green open access

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Abstract

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.

Type: Article
Title: Sequential Monte Carlo methods for Bayesian elliptic inverse problems
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s11222-015-9556-7
Publisher version: http://dx.doi.org/10.1007/s11222-015-9556-7
Language: English
Additional information: The final publication is available at Springer via http://dx.doi.org/10.1007/s11222-015-9556-7.
Keywords: Inverse problems, Elliptic PDEs, Groundwater flow, Adaptive SMC, Markov chain Monte Carlo
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: https://discovery.ucl.ac.uk/id/eprint/1471849
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