Copula density-driven metrics for sensitivity analysis: Theory and application to flow and transport in porous media

Abstract

We introduce original sensitivity analysis metrics with the aim of assistingdiagnosis of the functioning of a given model. We do so by characterizing model-induced dependencies between a target model output and selected model input(s) through the associated bivariate copuladensity. The latter fully characterizes the dependencies between two random variables at any order (i.e., without being limited to linear dependence), independent of the marginal behavior of the two variables. As a metric to assess sensitivity, we rely on the absolute distance betweenthe copuladensity associated with the target model output and a model input and its counterpart associated with two independent variables. We then provide two sensitivity indices which allow characterizing (i) the global (with respect to the input) value of the sensitivity and (ii) the degree of variability (across the range of the input values) of the sensitivity for each value that the prescribed model output can possibly undertake, as driven by the governing model. In this sense, our approach to sensitivity is global with respect to model input(s) and local with respect to model output, thus enabling one to discriminate the relevance of an input across the entire range of values of the modeling goal of interest. We exemplify the use of our approach and illustrate the type of information it can provide by focusing on an analytical test function and on two scenarios related to flow and transport in porous media.