Abstract

Co-authors: Andrew Stuart (Caltech) , Han Cheng Lie and Timm Sullivan (Free University Berlin)

We are interested in the inverse problem of estimating unknown parameters in a mathematical model from observed data. We follow the Bayesian approach, in which the solution to the inverse problem is the probability distribution of the unknown parameters conditioned on the observed data, the so-called posterior distribution. We are particularly interested in the case where the mathematical model is non-linear and expensive to simulate, for example given by a partial differential equation. We consider the use of surrogate models to approximate the Bayesian posterior distribution. We present a general framework for the analysis of the error introduced in the posterior distribution, and discuss particular examples of surrogate models such as Gaussian process emulators and randomised misfit approaches.