Derivative based global sensitivity analysis and its entropic link (2310.00551v3)
Abstract: Variance-based Sobol' sensitivity is one of the most well-known measures in global sensitivity analysis (GSA). However, uncertainties with certain distributions, such as highly skewed distributions or those with a heavy tail, cannot be adequately characterised using the second central moment only. Entropy-based GSA can consider the entire probability density function, but its application has been limited because it is difficult to estimate. Here we present a novel derivative-based upper bound for conditional entropies, to efficiently rank uncertain variables and to work as a proxy for entropy-based total effect indices. To overcome the non-desirable issue of negativity for differential entropies as sensitivity indices, we discuss an exponentiation of the total effect entropy and its proxy. Numerical verifications demonstrate that the upper bound is tight for monotonic functions and it provides the same input variable ranking as the entropy-based indices for about three-quarters of the 1000 random functions tested. We found that the new entropy proxy performs similarly to the variance-based proxies for a river flood physics model with 8 inputs of different distributions, and these two proxies are equivalent in the special case of linear functions with Gaussian inputs. We expect the new entropy proxy to increase the variable screening power of derivative-based GSA and to complement Sobol'-indices proxy for a more diverse type of distributions.
- Saltelli, A.: Global sensitivity analysis: the primer. John Wiley, 2008 http://books.google.at/books?id=wAssmt2vumgC. – ISBN 9780470059975
- Global sensitivity analysis based on entropy. In: Proceedings of the ESREL 2008 Conference (2008), S. 2107–2115
- Morris, Max D.: Factorial Sampling Plans for Preliminary Computational Experiments. In: Technometrics 33 (1991), Nr. 2, 161-174. http://dx.doi.org/10.1080/00401706.1991.10484804. – DOI 10.1080/00401706.1991.10484804
- Monte Carlo evaluation of derivative-based global sensitivity measures. In: Reliability Engineering & System Safety 94 (2009), Nr. 7, S. 1135–1148
- Campbell, L L.: Exponential entropy as a measure of extent of a distribution. In: Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 5 (1966), Nr. 3, S. 217–225
- Derivative based global sensitivity measures and their link with global sensitivity indices. In: Mathematics and Computers in Simulation 79 (2009), Nr. 10, S. 3009–3017
- Derivative-based global sensitivity measures: General links with Sobol’ indices and numerical tests. In: Mathematics and Computers in Simulation 87 (2013), 45-54. http://dx.doi.org/https://doi.org/10.1016/j.matcom.2013.02.002. – DOI https://doi.org/10.1016/j.matcom.2013.02.002. – ISSN 0378–4754
- Making sense of global sensitivity analyses. In: Computers & Geosciences 65 (2014), 84-94. http://dx.doi.org/https://doi.org/10.1016/j.cageo.2013.06.006. – DOI https://doi.org/10.1016/j.cageo.2013.06.006. – ISSN 0098–3004. – TOUGH Symposium 2012
- Sensitivity analysis: A review of recent advances. In: European Journal of Operational Research 248 (2016), Nr. 3, 869-887. http://dx.doi.org/https://doi.org/10.1016/j.ejor.2015.06.032. – DOI https://doi.org/10.1016/j.ejor.2015.06.032. – ISSN 0377–2217
- Density modification-based reliability sensitivity analysis. In: Journal of Statistical Computation and Simulation 85 (2015), Nr. 6, 1200-1223. http://dx.doi.org/10.1080/00949655.2013.873039. – DOI 10.1080/00949655.2013.873039
- Borgonovo, E.: A new uncertainty importance measure. In: Reliability Engineering & System Safety 92 (2007), Nr. 6, 771-784. http://dx.doi.org/https://doi.org/10.1016/j.ress.2006.04.015. – DOI https://doi.org/10.1016/j.ress.2006.04.015. – ISSN 0951–8320
- Yang, Jiannan: A general framework for probabilistic sensitivity analysis with respect to distribution parameters. In: Probabilistic Engineering Mechanics 72 (2023), S. 103433
- Yang, Jiannan: Decision-Oriented Two-Parameter Fisher Information Sensitivity Using Symplectic Decomposition. In: Technometrics 0 (2023), Nr. 0, 1-12. http://dx.doi.org/10.1080/00401706.2023.2216251. – DOI 10.1080/00401706.2023.2216251
- The future of sensitivity analysis: an essential discipline for systems modeling and policy support. In: Environmental Modelling & Software 137 (2021), S. 104954
- The battle of total-order sensitivity estimators. In: arXiv preprint arXiv:2009.01147 (2020)
- An effective screening design for sensitivity analysis of large models. In: Environmental modelling & software 22 (2007), Nr. 10, S. 1509–1518
- A simple and efficient method for global sensitivity analysis based on cumulative distribution functions. In: Environmental Modelling & Software 67 (2015), S. 1–11
- Relative entropy based method for probabilistic sensitivity analysis in engineering design. In: Journal of Mechanical Design 128 (2006), Nr. 2, S. 326–336
- Kala, Zdeněk: Global sensitivity analysis based on entropy: From differential entropy to alternative measures. In: Entropy 23 (2021), Nr. 6, S. 778
- Cover, Thomas M.: Elements of information theory. John Wiley & Sons, 1999
- Krzykacz-Hausmann, Bernard: Epistemic sensitivity analysis based on the concept of entropy. In: Proceedings of SAMO2001 (2001), S. 31–35
- Papoulis, Athanasios: Probability, random variables and stochastic processes. 1984
- On the information loss in memoryless systems: The multivariate case. In: arXiv preprint arXiv:1109.4856 (2011)
- On the similarity of the entropy power inequality and the Brunn-Minkowski inequality (corresp.). In: IEEE Transactions on Information Theory 30 (1984), Nr. 6, S. 837–839
- Support indices: Measuring the effect of input variables over their supports. In: Reliability Engineering & System Safety 187 (2019), S. 17–27
- A review on global sensitivity analysis methods. In: Uncertainty management in simulation-optimization of complex systems: algorithms and applications (2015), S. 101–122
- On the entropy of continuous probability distributions (corresp.). In: IEEE Transactions on Information Theory 24 (1978), Nr. 1, S. 120–122
- Properties of Shannon entropy for double truncated random variables and its applications. In: Journal of Statistical Theory and Applications 19 (2020), Nr. 2, S. 261–273
- Moddemeijer, Rudy: On estimation of entropy and mutual information of continuous distributions. In: Signal processing 16 (1989), Nr. 3, S. 233–248