Uncertainty Quantification by Random Measures and Fields

TL;DR

This paper introduces a comprehensive framework for uncertainty quantification using random measures and fields, enabling detailed sensitivity analysis and covariance decomposition for complex stochastic systems.

Contribution

It develops a unified approach to global sensitivity analysis and uncertainty quantification based on random counting measures and fields, integrating multiple uncertainty notions.

Findings

Decomposition of intensity measures and variances into subspaces.

Construction of positive random fields with covariance and sensitivity decompositions.

Application to interacting particle systems and integration with other uncertainty frameworks.

Abstract

We present a general framework for uncertainty quantification that is a mosaic of interconnected models. We define global first and second order structural and correlative sensitivity analyses for random counting measures acting on risk functionals of input-output maps. These are the ANOVA decomposition of the intensity measure and the decomposition of the random measure variance, each into subspaces. Orthogonal random measures furnish sensitivity distributions. We show that the random counting measure may be used to construct positive random fields, which admit decompositions of covariance and sensitivity indices and may be used to represent interacting particle systems. The first and second order global sensitivity analyses conveyed through random counting measures elucidate and integrate different notions of uncertainty quantification, and the global sensitivity analysis of random fields conveys the proportionate functional contributions to covariance. This framework complements others when used in conjunction with for instance algorithmic uncertainty and model selection uncertainty frameworks.