Functional ANOVA with Multiple Distributions: Implications for the Sensitivity Analysis of Computer Experiments

TL;DR

This paper investigates the properties of functional ANOVA expansions when multiple distributions are assigned to covariates, impacting sensitivity analysis in computer experiments.

Contribution

It provides a systematic analysis of existence, uniqueness, and properties of functional ANOVA expansions under multiple distributions, introducing a core of measures for guarantees.

Findings

Existence and uniqueness conditions for ANOVA with multiple distributions

New variance decomposition results under mixture models

Implications for global sensitivity analysis in computer experiments

Abstract

The functional ANOVA expansion of a multivariate mapping plays a fundamental role in statistics. The expansion is unique once a unique distribution is assigned to the covariates. Recent investigations in the environmental and climate sciences show that analysts may not be in a position to assign a unique distribution in realistic applications. We offer a systematic investigation of existence, uniqueness, orthogonality, monotonicity and ultramodularity of the functional ANOVA expansion of a multivariate mapping when a multiplicity of distributions is assigned to the covariates. In particular, we show that a multivariate mapping can be associated with a core of probability measures that guarantee uniqueness. We obtain new results for variance decomposition and dimension distribution under mixtures. Implications for the global sensitivity analysis of computer experiments are also discussed.