A COMPUTATIONAL MEASURE THEORETIC APPROACH TO INVERSE SENSITIVITY PROBLEMS II: A POSTERIORI ERROR ANALYSIS

被引：25
作者：
Butler, T. [1 ]
Estep, D. [2 ]
Sandelin, J. [3 ]
机构：
[1] Univ Texas Austin, Inst Computat Engn & Sci, Austin, TX 78712 USA
[2] Colorado State Univ, Dept Stat, Ft Collins, CO 80523 USA
[3] Colorado State Univ, Dept Math, Ft Collins, CO 80523 USA
来源：
SIAM JOURNAL ON NUMERICAL ANALYSIS | 2012年 / 50卷 / 01期
基金：
美国国家航空航天局; 美国国家科学基金会;
关键词：
a posteriori error analysis; adjoint problem; density estimation; inverse sensitivity analysis; nonparametric density estimation; sensitivity analysis; set-valued inverse; UNCERTAIN PARAMETERS; EVOLUTION;
D O I：
10.1137/100785958
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In part one of this paper [T. Butler and D. Estep, SIAM J. Numer. Anal., 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.
引用
收藏
页码：22 / 45
页数：24
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