Continuity of the Solution of a Non-Parametric Bayesian Statistical Calibration Procedure

TL;DR

This paper proves that a non-parametric Bayesian calibration method for computer models is mathematically stable, showing the solution's continuity with respect to input distributions, which supports its reliability in scientific applications.

Contribution

It establishes the uniform and weak continuity of the solution operator in a non-parametric Bayesian calibration framework, enhancing understanding of its stability.

Findings

Solution operator is uniformly continuous in total variation metric.

Solution operator is weakly continuous for broad distribution classes.

Supports the robustness of Bayesian calibration in scientific modeling.

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.