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We elaborate on results obtained in \cite{christen2018} for controlling thenumerical posterior error for Bayesian UQ problems, now considering forwardmaps arising from the solution of a semilinear evolution partial differentialequation. Results in \cite{christen2018} demand an estimate for the absoluteglobal error (AGE) of the numeric forward map. Our contribution is a numericalmethod for computing the AGE for semilinear evolution PDEs and shows thepotential applicability of \cite{christen2018} in this important wide rangefamily of PDEs. Numerical examples are given to illustrate the efficiency ofthe proposed method, obtaining numerical posterior distributions for unknownparameters that are nearly identical to the corresponding theoreticalposterior, by keeping their Bayes factor close to 1.

Error control in the numerical posterior distribution in the Bayesian UQ analysis of a semilinear evolution PDE