# Probabilistic Numerical Methods for PDE-constrained Bayesian Inverse Problems

@article{Cockayne2017ProbabilisticNM, title={Probabilistic Numerical Methods for PDE-constrained Bayesian Inverse Problems}, author={Jon Cockayne and Chris. J. Oates and Timothy John Sullivan and Mark A. Girolami}, journal={ArXiv}, year={2017}, volume={abs/1701.04006} }

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…

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