Moment-independent sensitivity analysis using copula.

Published on Feb 1, 2014in Risk Analysis2.564
· DOI :10.1111/risa.12110
Pengfei Wei11
Estimated H-index: 11
(NPU: Northwestern Polytechnical University),
Zhenzhou Lu21
Estimated H-index: 21
(NPU: Northwestern Polytechnical University),
Jingwen Song6
Estimated H-index: 6
(NPU: Northwestern Polytechnical University)
In risk assessment, the moment†independent sensitivity analysis (SA) technique for reducing the model uncertainty has attracted a great deal of attention from analysts and practitioners. It aims at measuring the relative importance of an individual input, or a set of inputs, in determining the uncertainty of model output by looking at the entire distribution range of model output. In this article, along the lines of Plischke et al., we point out that the original moment†independent SA index (also called delta index) can also be interpreted as the dependence measure between model output and input variables, and introduce another moment†independent SA index (called extended delta index) based on copula. Then, nonparametric methods for estimating the delta and extended delta indices are proposed. Both methods need only a set of samples to compute all the indices; thus, they conquer the problem of the “curse of dimensionality.†At last, an analytical test example, a risk assessment model, and the levelE model are employed for comparing the delta and the extended delta indices and testing the two calculation methods. Results show that the delta and the extended delta indices produce the same importance ranking in these three test examples. It is also shown that these two proposed calculation methods dramatically reduce the computational burden.
  • References (47)
  • Citations (20)
📖 Papers frequently viewed together
421 Citations
153 Citations
45 Citations
78% of Scinapse members use related papers. After signing in, all features are FREE.
#1Pengfei Wei (NPU: Northwestern Polytechnical University)H-Index: 11
#2Zhenzhou Lu (NPU: Northwestern Polytechnical University)H-Index: 21
Last. Changcong Zhou (NPU: Northwestern Polytechnical University)H-Index: 7
view all 4 authors...
Through several decades of development, global sensitivity analysis has been developed as a very useful guide tool for assessing scientific models and has gained pronounced attention in environmental science. However, standard global sensitivity analysis aims at measuring the contribution of input variables to model output uncertainty on average by investigating their full distribution ranges, but does not investigate the contribution of specific ranges. To deal with this problem, researchers ha...
15 CitationsSource
#1Elmar Plischke (TUC: Clausthal University of Technology)H-Index: 10
#2Emanuele Borgonovo (Bocconi University)H-Index: 26
Last. Curtis Smith (INL: Idaho National Laboratory)H-Index: 13
view all 3 authors...
153 CitationsSource
#1Pengfei Wei (NPU: Northwestern Polytechnical University)H-Index: 11
#2Zhenzhou Lu (NPU: Northwestern Polytechnical University)H-Index: 21
Last. Xiukai Yuan (NPU: Northwestern Polytechnical University)H-Index: 2
view all 3 authors...
The moment-independent sensitivity analysis (SA) is one of the most popular SA techniques. It aims at measuring the contribution of input variable(s) to the probability density function (PDF) of model output. However, compared with the variance-based one, robust and efficient methods are less available for computing the moment-independent SA indices (also called delta indices). In this paper, the Monte Carlo simulation (MCS) methods for moment-independent SA are investigated. A double-loop MCS m...
46 CitationsSource
#1Ivan Dimov (BAS: Bulgarian Academy of Sciences)H-Index: 20
#2Rayna Georgieva (BAS: Bulgarian Academy of Sciences)H-Index: 9
Last. Tzvetan Ostromsky (BAS: Bulgarian Academy of Sciences)H-Index: 7
view all 3 authors...
Abstract Variance-based approaches for global sensitivity analysis have been applied and analyzed to study the sensitivity of air pollutant concentrations according to variations of rates of chemical reactions. The Unified Danish Eulerian Model has been used as a mathematical model simulating a remote transport of air pollutants. Various Monte Carlo algorithms for numerical integration have been applied to compute Sobol's global sensitivity indices. A newly developed Monte Carlo algorithm based ...
10 CitationsSource
#1V. Gregory Weirs (SNL: Sandia National Laboratories)H-Index: 4
#2James R. Kamm (SNL: Sandia National Laboratories)H-Index: 10
Last. Michael S. Eldred (SNL: Sandia National Laboratories)H-Index: 25
view all 8 authors...
Sensitivity analysis is comprised of techniques to quantify the effects of the input variables on a set of outputs. In particular, sensitivity indices can be used to infer which input parameters most significantly affect the results of a computational model. With continually increasing computing power, sensitivity analysis has become an important technique by which to understand the behavior of large-scale computer simulations. Many sensitivity analysis methods rely on sampling from distribution...
25 CitationsSource
#1Pengfei Wei (NPU: Northwestern Polytechnical University)H-Index: 11
#2Zhenzhou Lu (NPU: Northwestern Polytechnical University)H-Index: 21
Last. Bintuan Wang (Aviation Industry Corporation of China)H-Index: 4
view all 5 authors...
Abstract An important problem in structure reliability analysis is how to reduce the failure probability. In this work, we introduce a main and total effect indices framework of global reliability sensitivity. By decreasing the uncertainty of input variables with high main effect indices, the most reduction of failure probability can be obtained. By decreasing the uncertainty of the input variables with small total effect indices (close to zero), the failure probability will not be reduced signi...
52 CitationsSource
#1Emanuele Borgonovo (Bocconi University)H-Index: 26
#2W. Castaings (University of Toulouse)H-Index: 3
Last. Stefano Tarantola (Institute for the Protection and Security of the Citizen)H-Index: 45
view all 3 authors...
Moment-independent sensitivity methods are attracting increasing attention among practitioners, since they provide a thorough way of investigating the sensitivity of model output under uncertainty. However, their estimation is challenging, especially in the presence of computationally intensive models. We argue that replacement of the original model by a metamodel can contribute in lowering the computation burden. A numerical estimation procedure is set forth. The procedure is first tested on an...
104 CitationsSource
#1Leming Qu (BSU: Boise State University)H-Index: 7
#2Wotao Yin (Rice University)H-Index: 53
A copula density is the joint probability density function (PDF) of a random vector with uniform marginals. An approach to bivariate copula density estimation is introduced that is based on maximum penalized likelihood estimation (MPLE) with a total variation (TV) penalty term. The marginal unity and symmetry constraints for copula density are enforced by linear equality constraints. The TV-MPLE subject to linear equality constraints is solved by an augmented Lagrangian and operator-splitting al...
18 CitationsSource
#1Paola AnnoniH-Index: 11
#2Rainer Brüggemann (Leibniz Association)H-Index: 31
Last. Andrea SaltelliH-Index: 52
view all 3 authors...
Partial order tools can be used in multiple criteria analysis to prioritize and rank a set of objects. In this setting the starting point is generally a matrix M"n"x"k of k observed indicators on n objects. Given that indicators are measured at least at the ordinal level, from matrix M its corresponding partially ordered set - poset - is set up to form the basis of multi-criteria ranking. The partial order may be very complex even when the number of objects to be compared is relatively small. Th...
44 CitationsSource
#2William CastaingsH-Index: 1
Last. Stephano Tarantola (Institute for the Protection and Security of the Citizen)H-Index: 1
view all 3 authors...
Moment independent methods for the sensitivity analysis of model output are attracting growing attention among both academics and practitioners. However, the lack of benchmarks against which to compare numerical strategies forces one to rely on ad hoc experiments in estimating the sensitivity measures. This article introduces a methodology that allows one to obtain moment independent sensitivity measures analytically. We illustrate the procedure by implementing four test cases with different...
94 CitationsSource
Cited By20
#1Tatsuya Sakurahara (UIUC: University of Illinois at Urbana–Champaign)H-Index: 5
#2Seyed Reihani (UIUC: University of Illinois at Urbana–Champaign)H-Index: 5
Last. Zahra Mohaghegh (UIUC: University of Illinois at Urbana–Champaign)H-Index: 7
view all 4 authors...
An integrated probabilistic risk assessment framework combines spatio-temporal probabilistic simulations of underlying failure mechanisms with classical probabilistic risk assessment logic consisti...
1 CitationsSource
#1Isadora Antoniano-Villalobos (Ca' Foscari University of Venice)H-Index: 3
#2Emanuele Borgonovo (Bocconi University)H-Index: 26
Last. Xuefei Lu (Bocconi University)H-Index: 1
view all 3 authors...
Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest. Simulation complexity, large dimensionality and long running times may force analysts to make statistical inference at small sample sizes. Methods designed to estimate probabilistic sensitivity measures at relatively low computational costs are attracting increa...
#1Xinyao LiH-Index: 1
Last. Liangli HeH-Index: 1
view all 3 authors...
#1Longxue He (Leibniz University of Hanover)
#2Michael Beer (Leibniz University of Hanover)H-Index: 20
Last. António Topa Gomes (University of Porto)H-Index: 4
view all 5 authors...
Bayesian Network (BN) is an efficient model tool for approximate reasoning based on machine learning. It has been widely used for supporting the decision in many engineering applications such as geotechnical engineering. However, the current studies on BN are mostly on uncertainty quantification and decision-making, while the sensitivity analysis on BN, which may provide much more insights for decision-making, has not received much attention. The current research on sensitivity analysis of BN ma...
#1Jingwen Song (NPU: Northwestern Polytechnical University)H-Index: 6
#2Pengfei Wei (NPU: Northwestern Polytechnical University)H-Index: 11
Last. Zuxiang Lei (ECJTU: East China Jiaotong University)
view all 7 authors...
Abstract Non-intrusive Imprecise Stochastic Simulation (NISS) is a recently developed general methodological framework for efficiently propagating the imprecise probability models and for estimating the resultant failure probability functions and bounds. Due to the simplicity, high efficiency, stability and good convergence, it has been proved to be one of the most appealing forward uncertainty quantification methods. However, the current version of NISS is only applicable for model with input v...
In reliability-based design, the estimation of the failure probability is a crucial objective. However, focusing only on the occurrence of the failure event may be insufficient to entirely characterize the reliability of the considered system. This paper provides a common estimation scheme of two complementary moment independent sensitivity measures, allowing to improve the understanding of the system's reliability. Numerical applications are performed in order to show the effectiveness of the p...
#1Luyi Li (NPU: Northwestern Polytechnical University)H-Index: 7
#2Yushan Liu (NPU: Northwestern Polytechnical University)
Last. Zhenzhou Lu (NPU: Northwestern Polytechnical University)H-Index: 21
view all 3 authors...
Abstract This paper presents a new dependence measure for importance analysis based on multivariate probability integral transformation (MPIT), which can assess the effect of an individual input, or a group of inputs on the whole uncertainty of model output. The mathematical properties of the new measure are derived and discussed. The nonparametric method for estimating the new measure is presented. The effectiveness of the new measure is compared with the well-known delta and extended delta ind...
Abstract Copula theory is concerned with defining dependence structures given appropriate marginal distributions. Probabilistic sensitivity analysis is concerned with quantifying the strength of the dependence among the output of a simulator and the uncertain simulator inputs. In this work, we investigate the connection between these two families of methods. We define four classes of sensitivity measures based on the distance between the empirical copula and the product copula. We discuss the ne...