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.

中文翻译：

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半线性演化偏微分方程贝叶斯 UQ 分析中数值后验分布的误差控制

我们详细说明了在 \cite{christen2018} 中获得的结果，用于控制贝叶斯 UQ 问题的数值后验误差，现在考虑由半线性演化偏微分方程的解产生的正向映射。\cite{christen2018} 中的结果要求对 FM 的数值解进行误差估计。我们的贡献是一种计算半线性演化 PDE 的事后（即后验）误差估计的数值方法，并展示了 \cite{christen2018} 在这个重要的广泛 PDE 系列中的潜在适用性。给出了数值例子来说明所提出方法的效率，通过保持其贝叶斯因子接近 1，获得与相应理论后验几乎相同的未知参数的数值后验分布。