  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 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 \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.
