Uncertainty-based sensitivity indices for imprecise probability distributions

Abstract

An uncertainty-based sensitivity index represents the contribution that uncertainty in model input X i makes to the uncertainty in model output Y. This paper addresses the situation where the uncertainties in the model inputs are expressed as closed convex sets of probability measures, a situation that exists when inputs are expressed as intervals or sets of intervals with no particular distribution specified over the intervals, or as probability distributions with interval-valued parameters. Three different approaches to measuring uncertainty, and hence uncertainty-based sensitivity, are explored. Variance-based sensitivity analysis (VBSA) estimates the contribution that each uncertain input, acting individually or in combination, makes to variance in the model output. The partial expected value of perfect information (partial EVPI), quantifies the (financial) value of learning the true numeric value of an input. For both of these sensitivity indices the generalization to closed convex sets of probability measures yields lower and upper sensitivity indices. Finally, the use of relative entropy as an uncertainty-based sensitivity index is introduced and extended to the imprecise setting, drawing upon recent work on entropy measures for imprecise information.