Uncertainty and sensitivity analysis in the presence of stochastic and subjective uncertainty

Abstract

Uncertainty and sensitivity analyses for systems that involve both stochastic (i.e., aleatory) and subjective (i.e., epistemic) uncertainty are discussed. In such analyses, the dependent variable is usually a complementary cumulative distribution function (CCDF) that arises from stochastic uncertainty; uncertainty analysis involves the determination of a distribution of CCDFs that results from subjective uncertainty, and sensitivity analysis involves the determination of the effects of subjective uncertainty in individual variables on this distribution of CCDFs. Uncertainty analysis is presented as an integration problem involving probability spaces for stochastic and subjective uncertainty. Approximation procedures for the underlying integrals are described that provide an assessment of the effects of stochastic uncertainty, an assessment of the effects of subjective uncertainty, and a basis for performing sensitivity studies. Extensive use is made of Latin hypercube sampling, importance sampling and regression-based sensitivity analysis techniques. The underlying ideas, which are initially presented in an abstract form, are central to the design and performance of real analyses. To emphasize the connection between concept and computational practice, these ideas are illustrated with an analysis involving the MACCS reactor accident consequence model a, performance assessment for the Waste Isolation Pilot Plant, and a probabilistic risk assessment for a nuclear power station.