Statistical inference for Sobol pick-freeze Monte Carlo method

Many mathematical models involve input parameters, which are not precisely known. Global sensitivity analysis aims to identify the parameters whose uncertainty has the largest impact on the variability of a quantity of interest (output of the model). One of the statistical tools used to quantify the...

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Bibliographic Details
Published in:Statistics (Berlin, DDR) DDR), 2016-07, Vol.50 (4), p.881-902
Main Authors: Gamboa, F., Janon, A., Klein, T., Lagnoux, A., Prieur, C.
Format: Article
Language:English
Subjects:
Applications
Asymptotic properties
Berry-Esseen theorem
Computer simulation
concentration inequalities
Confidence intervals
Economic models
Mathematical models
Mathematics
Methodology
Monte Carlo simulation
Parameter identification
Parameter sensitivity
Parameter uncertainty
Parameters
Sensitivity analysis
Sobol indices
Statistical analysis
Statistical inference
Statistics
Statistics Theory
tests
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Summary:Many mathematical models involve input parameters, which are not precisely known. Global sensitivity analysis aims to identify the parameters whose uncertainty has the largest impact on the variability of a quantity of interest (output of the model). One of the statistical tools used to quantify the influence of each input variable on the output is the Sobol sensitivity index. We consider the statistical estimation of this index from a finite sample of model outputs. We study asymptotic and non-asymptotic properties of two estimators of Sobol indices. These properties are applied to significance tests and estimation by confidence intervals.
ISSN:0233-1888
1029-4910
DOI:10.1080/02331888.2015.1105803