ERROR CONTROL IN THE NUMERICAL POSTERIOR DISTRIBUTION IN THE BAYESIAN UQ ANALYSIS OF A SEMILINEAR EVOLUTION PDE

Abstract

We elaborate on results obtained in \cite{christen2018} for controlling the numerical posterior error for Bayesian UQ problems, now considering forward maps arising from the solution of a semilinear evolution partial differential equation. Results in \cite{christen2018} demand an error estimate for the numerical solution of the FM. Our contribution is a numerical method for computing after-the-fact (i.e. a posteriori) error estimates for semilinear evolution PDEs, and show the potential applicability of \cite{christen2018} in this important wide range family of PDEs. Numerical examples are given to illustrate the efficiency of the proposed method, obtaining numerical posterior distributions for unknown parameters that are nearly identical to the corresponding theoretical posterior, by keeping their Bayes factor close to 1.