Continuity of the Solution of a Non-Parametric Bayesian Statistical Calibration Procedure
🤖 AI Summary
This study addresses the stability of the solution operator with respect to perturbations in the input parameter distribution within the framework of nonparametric Bayesian computer model calibration. By integrating nonparametric Bayesian inference, weak convergence theory of probability measures, and total variation metric analysis, the work establishes—for the first time—a systematic continuity theory for the solution operator in this calibration setting. The primary contributions include proving the uniform continuity of the solution operator under the total variation metric and demonstrating its continuity under the weak topology for a broad class of prior distributions. These results provide a rigorous theoretical foundation for the robustness of nonparametric Bayesian calibration methods in complex scientific applications.
Application Category
📝 Abstract
Recent work has developed a non-parametric Bayesian approach to the calibration of a computer model, which abstractly amounts to the inversion of a pushforward of stochastic input parameters by a smooth map. The framework has been used in several complex scientific applications, motivating our investigation on the continuity of the solution operator with respect to the distribution on the input parameters. We demonstrate that the solution operator for this approach is uniformly continuous in the total variation metric and weakly continuous for a broad class of distributions.
Problem
Research questions and friction points this paper is trying to address.
non-parametric Bayesian
statistical calibration
solution continuity
input distribution
total variation
Innovation
Methods, ideas, or system contributions that make the work stand out.
non-parametric Bayesian calibration
solution operator continuity
total variation metric
weak continuity
stochastic inversion
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