TY - CHAP A1 - Sullivan, T. J. T1 - Well-posedness of Bayesian inverse problems in quasi-Banach spaces with stable priors T2 - 88th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Weimar 2017 Y1 - 2017 U6 - https://doi.org/10.1002/pamm.201710402 VL - 17 IS - 1 SP - 871 EP - 874 ER - TY - CHAP A1 - Cockayne, Jon A1 - Oates, Chris A1 - Sullivan, T. J. A1 - Girolami, Mark T1 - Probabilistic Numerical Methods for PDE-constrained Bayesian Inverse Problems T2 - Proceedings of the 36th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering N2 - 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 Y1 - 2017 U6 - https://doi.org/10.1063/1.4985359 VL - 1853 SP - 060001-1 EP - 060001-8 ER - TY - CHAP A1 - Teymur, Onur A1 - Lie, Han Cheng A1 - Sullivan, T. J. A1 - Calderhead, Ben T1 - Implicit probabilistic integrators for ODEs T2 - Advances in Neural Information Processing Systems 31 (NIPS 2018) Y1 - 2018 UR - http://papers.nips.cc/paper/7955-implicit-probabilistic-integrators-for-odes ER -