SIAM Journal on Numerical Analysis
Perception as Bayesian inference
Perception as Bayesian inference
Computational Differential Equations
Computational Differential Equations
Monte Carlo Statistical Methods (Springer Texts in Statistics)
Monte Carlo Statistical Methods (Springer Texts in Statistics)
Inverse Problem Theory and Methods for Model Parameter Estimation
Inverse Problem Theory and Methods for Model Parameter Estimation
Journal of Computational Physics
An A Posteriori-A Priori Analysis of Multiscale Operator Splitting
SIAM Journal on Numerical Analysis
Computational measure theoretic approach to inverse sensitivity analysis: methods and analysis
Computational measure theoretic approach to inverse sensitivity analysis: methods and analysis
Blockwise Adaptivity for Time Dependent Problems Based on Coarse Scale Adjoint Solutions
SIAM Journal on Scientific Computing
A Posteriori Error Analysis of Stochastic Differential Equations Using Polynomial Chaos Expansions
SIAM Journal on Scientific Computing
A Posteriori Error Analysis of Parameterized Linear Systems Using Spectral Methods
SIAM Journal on Matrix Analysis and Applications
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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.