Monte Carlo algorithms for evaluating Sobol' sensitivity indices

Authors:
I. Dimov;R. Georgieva
Affiliations:
Department of Parallel Algorithms, Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev 25 A, 1113 Sofia, Bulgaria and Centre for Advanced Computing and Emerging Tech ...;Department of Parallel Algorithms, Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev 25 A, 1113 Sofia, Bulgaria
Venue:
Mathematics and Computers in Simulation
Year:
2010

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Abstract

Sensitivity analysis is a powerful technique used to determine robustness, reliability and efficiency of a model. The main problem in this procedure is the evaluating total sensitivity indices that measure a parameter's main effect and all the interactions involving that parameter. From a mathematical point of view this problem is presented by a set of multidimensional integrals. In this work a simple adaptive Monte Carlo technique for evaluating Sobol' sensitivity indices is developed. A comparison of accuracy and complexity of plain Monte Carlo and adaptive Monte Carlo algorithms is presented. Numerical experiments for evaluating integrals of different dimensions are performed.