ABSTRACT
This work investigates aspects of the global sensitivity analysis of computer codes when alternative plausible distributions for the model inputs are available to the analyst. Analysts may decide to explore results under each distribution or to aggregate the distributions, assigning, for instance, a mixture. In the first case, we lose uniqueness of the sensitivity measures, and in the second case, we lose independence even if the model inputs are independent under each of the assigned distributions. Removing the unique distribution assumption impacts the mathematical properties at the basis of variance-based sensitivity analysis and has consequences on result interpretation as well. We analyze in detail the technical aspects. From this investigation, we derive corresponding recommendations for the risk analyst. We show that an approach based on the generalized functional ANOVA expansion remains theoretically grounded in the presence of a mixture distribution. Numerically, we base the construction of the generalized function ANOVA effects on the diffeomorphic modulation under observable response preserving homotopy regression. Our application addresses the calculation of variance-based sensitivity measures for the well-known Nordhaus' DICE model, when its inputs are assigned a mixture distribution. A discussion of implications for the risk analyst and future research perspectives closes the work.
ABSTRACT
Quantitative models support investigators in several risk analysis applications. The calculation of sensitivity measures is an integral part of this analysis. However, it becomes a computationally challenging task, especially when the number of model inputs is large and the model output is spread over orders of magnitude. We introduce and test a new method for the estimation of global sensitivity measures. The new method relies on the intuition of exploiting the empirical cumulative distribution function of the simulator output. This choice allows the estimators of global sensitivity measures to be based on numbers between 0 and 1, thus fighting the curse of sparsity. For density-based sensitivity measures, we devise an approach based on moving averages that bypasses kernel-density estimation. We compare the new method to approaches for calculating popular risk analysis global sensitivity measures as well as to approaches for computing dependence measures gathering increasing interest in the machine learning and statistics literature (the Hilbert-Schmidt independence criterion and distance covariance). The comparison involves also the number of operations needed to obtain the estimates, an aspect often neglected in global sensitivity studies. We let the estimators undergo several tests, first with the wing-weight test case, then with a computationally challenging code with up to k = 30 , 000 inputs, and finally with the traditional Level E benchmark code.
ABSTRACT
Measures of sensitivity and uncertainty have become an integral part of risk analysis. Many such measures have a conditional probabilistic structure, for which a straightforward Monte Carlo estimation procedure has a double-loop form. Recently, a more efficient single-loop procedure has been introduced, and consistency of this procedure has been demonstrated separately for particular measures, such as those based on variance, density, and information value. In this work, we give a unified proof of single-loop consistency that applies to any measure satisfying a common rationale. This proof is not only more general but invokes less restrictive assumptions than heretofore in the literature, allowing for the presence of correlations among model inputs and of categorical variables. We examine numerical convergence of such an estimator under a variety of sensitivity measures. We also examine its application to a published medical case study.
