Posterior distribution existence and error control in Banach spaces in the Bayesian approach to UQ in inverse problems

Strong convergence rates of probabilistic integrators for ordinary differential equations

“…However, for applications to inverse problems and data assimilation, in which the numerical solution of the (1.1) is used to (approximately) evaluate the data misfit or likelhood, an alternative paradigm is to directly examine the impact of discretisation upon the quality of later inferences using e.g. Bayes factors [2,4]. There is also the well-established literature of information-based complexity and average-case analysis, with its greater emphasis on algorithmic aspects such as computational cost and optimal accuracy for given classes of information [25,32,41,40].…”