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

摘要

We elaborate on results previously obtained 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. These results demand an estimate for the absolute global error (AGE) of the numeric forward map. Our contribution is a numerical method for computing the AGE for semilinear evolution PDEs and shows the potential applicability of our results 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.