论文标题
半线性进化PDE的贝叶斯UQ分析中数值后验分布中的误差控制
Error control in the numerical posterior distribution in the Bayesian UQ analysis of a semilinear evolution PDE
论文作者
论文摘要
我们详细介绍了在\ cite {Christen2018}中获得的结果，用于控制贝叶斯UQ问题的数值后误差，现在考虑到由半线性进化部分偏微分方程解决方案引起的前进图。结果\ cite {Christen2018}要求对数字前向图的绝对全局误差（年龄）进行估计。我们的贡献是一种计算半线性进化PDE年龄的数值方法，并显示了在这个重要的广泛范围的PDE家族中\ cite {Christen2018}的潜在适用性。给出了数值示例，以说明所提出的方法的效率，通过使其贝叶斯因子接近1，获得了未知参数的数值后验分布。
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.
