Fighting the curse of sparsity: probabilistic sensitivity measures from cumulative distribution functions

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

Computing Shapley Effects for Sensitivity Analysis

Shapley effects are attracting increasing attention as sensitivity measures. When the value function is the conditional variance, they account for the individual and higher order effects of a model input. They are also well defined under model input dependence. However, one of the issues associated with their use is computational cost. We present a new algorithm that offers major improvements for the computation of Shapley effects, reducing computational burden by several orders of magnitude (from $k!\cdot k$ to $2^k$, where $k$ is the number of inputs) with respect to currently available implementations. The algorithm works in the presence of input dependencies. The algorithm also makes it possible to estimate all generalized (Shapley-Owen) effects for interactions.Comment: 16 pages, 5 figures, 3 tables, 2 algorithm

The Future of Sensitivity Analysis: An essential discipline for systems modeling and policy support

Sensitivity analysis (SA) is en route to becoming an integral part of mathematical modeling. The tremendous potential benefits of SA are, however, yet to be fully realized, both for advancing mechanistic and data-driven modeling of human and natural systems, and in support of decision making. In this perspective paper, a multidisciplinary group of researchers and practitioners revisit the current status of SA, and outline research challenges in regard to both theoretical frameworks and their applications to solve real-world problems. Six areas are discussed that warrant further attention, including (1) structuring and standardizing SA as a discipline, (2) realizing the untapped potential of SA for systems modeling, (3) addressing the computational burden of SA, (4) progressing SA in the context of machine learning, (5) clarifying the relationship and role of SA to uncertainty quantification, and (6) evolving the use of SA in support of decision making. An outlook for the future of SA is provided that underlines how SA must underpin a wide variety of activities to better serve science and society.John Jakeman’s work was supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Scientific Discovery through Advanced Computing (SciDAC) program. Joseph Guillaume received funding from an Australian Research Council Discovery Early Career Award (project no. DE190100317). Arnald Puy worked on this paper on a Marie Sklodowska-Curie Global Fellowship, grant number 792178. Takuya Iwanaga is supported through an Australian Government Research Training Program (AGRTP) Scholarship and the ANU Hilda-John Endowment Fun

The future of sensitivity analysis: an essential discipline for systems modeling and policy support

Sensitivity analysis (SA) is en route to becoming an integral part of mathematical modeling. The tremendous potential benefits of SA are, however, yet to be fully realized, both for advancing mechanistic and data-driven modeling of human and natural systems, and in support of decision making. In this perspective paper, a multidisciplinary group of researchers and practitioners revisit the current status of SA, and outline research challenges in regard to both theoretical frameworks and their applications to solve real-world problems. Six areas are discussed that warrant further attention, including (1) structuring and standardizing SA as a discipline, (2) realizing the untapped potential of SA for systems modeling, (3) addressing the computational burden of SA, (4) progressing SA in the context of machine learning, (5) clarifying the relationship and role of SA to uncertainty quantification, and (6) evolving the use of SA in support of decision making. An outlook for the future of SA is provided that underlines how SA must underpin a wide variety of activities to better serve science and society

Transient Effects of Linear Dynamical Systems

This work discusses the behavior of linear continuous-time dynamical systems on small and medium-sized time-scales, i.e., before asymptotic effects rule the system's behavior.A general theoretical framework is established in this work. Some special cases are studied, in particular, time-delay systems and positive systems. These studies give rise to certain Lyapunov-functionswhich can be used to estimate the transient behavior of the system.The synthesis of feedback-controllers which satify certain given transientbounds is also considered

Transiente Effekte linearer dynamischer Systeme

This work discusses the behavior of linear continuous-time dynamical systems on small and medium-sized time-scales, i.e., before asymptotic effects rule the system's behavior.A general theoretical framework is established in this work. Some special cases are studied, in particular, time-delay systems and positive systems. These studies give rise to certain Lyapunov-functionswhich can be used to estimate the transient behavior of the system.The synthesis of feedback-controllers which satify certain given transientbounds is also considered

1.2 Properties of Norms.............................. 8

– Dr. rer. nat.