Butler T, Estep D, Sandelin J
Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, TX 78712 (
SIAM J Numer Anal. 2012;50(1):22-45. doi: 10.1137/100785958.
In part one of this paper [T. Butler and D. Estep, , to appear], we develop and analyze a numerical method to solve a probabilistic inverse sensitivity analysis problem for a smooth deterministic map assuming that the map can be evaluated exactly. In this paper, we treat the situation in which the output of the map is determined implicitly and is difficult and/or expensive to evaluate, e.g., requiring the solution of a differential equation, and hence the output of the map is approximated numerically. The main goal is an a posteriori error estimate that can be used to evaluate the accuracy of the computed distribution solving the inverse problem, taking into account all sources of statistical and numerical deterministic errors. We present a general analysis for the method and then apply the analysis to the case of a map determined by the solution of an initial value problem.
在本文的第一部分[T. 巴特勒和D. 埃斯特普，即将发表]中，我们开发并分析了一种数值方法，用于求解光滑确定性映射的概率逆灵敏度分析问题，假设该映射可以精确求值。在本文中，我们处理映射输出由隐式确定且求值困难和/或成本高昂的情况，例如需要求解一个微分方程，因此映射的输出通过数值近似。主要目标是一个后验误差估计，可用于评估求解逆问题的计算分布的准确性，同时考虑到所有统计和数值确定性误差来源。我们对该方法进行了一般分析，然后将分析应用于由初值问题的解确定的映射的情况。
