Probabilistic numerical methods for PDE-constrained Bayesian inverse problems

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Conference object , Other literature type 01 Jan 2017Embargo end date: 01 Jan 2017Publisher:Author(s)Journal:AIP Conference Proceedings, volume 1,853, page 60,001 (issn: 0094-243X,

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Authors: Jon Cockayne; Chris J. Oates; Tim Sullivan 0001; Mark A. Girolami;

doi: 10.1063/1.4985359 , 10.48550/arxiv.1701.04006

arXiv: 1701.04006

Probabilistic numerical methods for PDE-constrained Bayesian inverse problems

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Abstract

This paper develops meshless methods for probabilistically describing discretisation error in the numerical solution of partial differential equations. This construction enables the solution of Bayesian inverse problems while accounting for the impact of the discretisation of the forward problem. In particular, this drives statistical inferences to be more conservative in the presence of significant solver error. Theoretical results are presented describing rates of convergence for the posteriors in both the forward and inverse problems. This method is tested on a challenging inverse problem with a nonlinear forward model.

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Freie Universität Berlin
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Keywords

Methodology (stat.ME), FOS: Computer and information sciences, FOS: Mathematics, Mathematics - Statistics Theory, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), Statistics Theory (math.ST), QA, Statistics - Methodology

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