@inproceedings{CockayneOatesSullivanetal., author = {Cockayne, Jon and Oates, Chris and Sullivan, T. J. and Girolami, Mark}, title = {Probabilistic Numerical Methods for PDE-constrained Bayesian Inverse Problems}, series = {Proceedings of the 36th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering}, volume = {1853}, booktitle = {Proceedings of the 36th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering}, doi = {10.1063/1.4985359}, pages = {060001-1 -- 060001-8}, 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}, language = {en} } @inproceedings{TeymurLieSullivanetal., author = {Teymur, Onur and Lie, Han Cheng and Sullivan, T. J. and Calderhead, Ben}, title = {Implicit probabilistic integrators for ODEs}, series = {Advances in Neural Information Processing Systems 31 (NIPS 2018)}, booktitle = {Advances in Neural Information Processing Systems 31 (NIPS 2018)}, language = {en} } @inproceedings{Sullivan, author = {Sullivan, T. J.}, title = {Well-posedness of Bayesian inverse problems in quasi-Banach spaces with stable priors}, series = {88th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Weimar 2017}, volume = {17}, booktitle = {88th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Weimar 2017}, number = {1}, doi = {10.1002/pamm.201710402}, pages = {871 -- 874}, language = {en} }