Monte Carlo estimators for small sensitivity indices

Sobol, I. M.; Myshetskaya, E. E.

doi:10.1515/mcma.2007.023

Cited by 46 publications

(35 citation statements)

References 4 publications

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“…As an example, the numerical results obtained for sensitivity study of ammonia concentrations with respect to emission levels in the area of Milan in January 1997 are the following: a) 0 ≈ 0 048 and 2 0 ≈ 0 002, respectively; b) the total variance D ≈ 0 038, and the partial variances The comparatively small values of 0 give an assumption that the correlated sampling approach could be efficient, see [22]. A number of numerical experiments have been performed applying the correlated sampling and combined approach.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…The issue about parameter importance can be studied via numerical integration in the terms of analysis of variance (ANOVA). A number of unbiased Monte Carlo estimators for global sensitivity indices have been developed applying the ANOVA-decomposition of a model function [11,19,21,22].…”

Section: The Sobol' Approach For Sensitivity Analysismentioning

confidence: 99%

“…An approach that combines ideas of reducing of the mean value and the correlated sampling has been suggested in [22]. Again the idea consists in an original integrand shift with a constant ∼ 0 , i.e.…”

Section: The Sobol' Approach For Sensitivity Analysismentioning

confidence: 99%

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Sensitivity studies of pollutant concentrations calculated by the UNI-DEM with respect to the input emissions

et al. 2013

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The influence of emission levels on the concentrations of four important air pollutants (ammonia, ozone, ammonium sulphate and ammonium nitrate) over three European cities (Milan, Manchester, and Edinburgh) with different geographical locations is considered. Sensitivity analysis of the output of the Unified Danish Eulerian Model according to emission levels is provided. The Sobol' variance-based approach for global sensitivity analysis has been applied to compute the corresponding sensitivity measures. To measure the influence of the variation of emission levels over the pollutants concentrations the Sobol' global sensitivity indices are estimated using efficient techniques for small sensitivity indices to avoid the effect of loss of accuracy. Theoretical studies, as well as, practical computations are performed in order to analyze efficiency of various variance reduction techniques for computing small indices. The importance of accurate estimation of small sensitivity indices is analyzed. It is shown that the correlated sampling technique for small sensitivity indices gives reliable results for the full set of indices. Its superior efficiency is studied in details.

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Section: Numerical Results and Discussionmentioning

confidence: 99%

Section: The Sobol' Approach For Sensitivity Analysismentioning

confidence: 99%

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Sensitivity studies of pollutant concentrations calculated by the UNI-DEM with respect to the input emissions

et al. 2013

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“…CMC pushes much of the variance to the projections over one and two dimensions. The variance components σ 2 u were estimated using the algorithm of [63] with RQMC (100 independent shifts of a lattice rule with n = 2 20 − 3 points); see [35,Section 8] for the details. The bounds (3) and (10) are useless here because the mixed derivatives are not defined everywhere, so the variation is infinite.…”

Section: A Stochastic Activity Networkmentioning

confidence: 99%

Randomized Quasi-Monte Carlo: An Introduction for Practitioners

L’Ecuyer

2018

Springer Proceedings in Mathematics &Amp; Statistics

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We survey basic ideas and results on randomized quasi-Monte Carlo (RQMC) methods, discuss their practical aspects, and give numerical illustrations. RQMC can improve accuracy compared with standard Monte Carlo (MC) when estimating an integral interpreted as a mathematical expectation. RQMC estimators are unbiased and their variance converges at a faster rate (under certain conditions) than MC estimators, as a function of the sample size. Variants of RQMC also work for the simulation of Markov chains, for function approximation and optimization, for solving partial differential equations, etc. In this introductory survey, we look at how RQMC point sets and sequences are constructed, how we measure their uniformity, why they can work for high-dimensional integrals, and how can they work when simulating Markov chains over a large number of steps.

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“…Sample estimates for the main and total effect indices are adapted from the equations proposed in refs. [13,14]. The second method available in NESSUS is the Fourier Amplitude Sensitivity Test (FAST) [15].…”

Section: Nessus Global Sensitivity Analysismentioning

confidence: 99%