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SIAM J. Numer. Anal. 50, pp. 22-45 (24 pages)
A Computational Measure Theoretic Approach to Inverse Sensitivity Problems II: A Posteriori Error Analysis
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Add to FacebookIn 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.
© 2012 Society for Industrial and Applied Mathematics
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Received February 16, 2010
Accepted September 29, 2011
Published online January 19, 2012
Accepted September 29, 2011
Published online January 19, 2012
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