Estimating sensitivity indices based on Gaussian process metamodels with compactly supported correlation functions
Estimating sensitivity indices based on Gaussian process metamodels with compactly supported correlation functions
Specific formulae are derived for quadrature-based estimators of global sensitivity indices when the unknown function can be modeled by a regression plus stationary Gaussian process using the Gaussian, Bohman, or cubic correlation functions. Estimation formulae are derived for the computation of process-based Bayesian and empirical Bayesian estimates of global sensitivity indices when the observed data are the function values corrupted by noise. It is shown how to restrict the parameter space for the compactly supported Bohman and cubic correlation functions so that (at least) a given proportion of the training data correlation entries are zero. This feature is important in the situation where the set of training data is large. The estimation methods are illustrated and compared via examples.
Svenson, Joshua
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Santner, Thomas
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Dean, Angela M.
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Moon, Hyejung
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Svenson, Joshua
e2cea0a1-a6f3-482a-87a7-9f70628c37ea
Santner, Thomas
961fb7d2-bd64-4f1b-8f85-cb23fc544cfd
Dean, Angela M.
9c90540a-cdf4-44ce-9d34-6b7b495a1ea3
Moon, Hyejung
486b8369-2c4c-49e8-8239-5e1d25993e3f
Svenson, Joshua, Santner, Thomas, Dean, Angela M. and Moon, Hyejung
(2013)
Estimating sensitivity indices based on Gaussian process metamodels with compactly supported correlation functions.
Journal of Statistical Planning and Inference.
(doi:10.1016/j.jspi.2013.04.003).
Abstract
Specific formulae are derived for quadrature-based estimators of global sensitivity indices when the unknown function can be modeled by a regression plus stationary Gaussian process using the Gaussian, Bohman, or cubic correlation functions. Estimation formulae are derived for the computation of process-based Bayesian and empirical Bayesian estimates of global sensitivity indices when the observed data are the function values corrupted by noise. It is shown how to restrict the parameter space for the compactly supported Bohman and cubic correlation functions so that (at least) a given proportion of the training data correlation entries are zero. This feature is important in the situation where the set of training data is large. The estimation methods are illustrated and compared via examples.
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e-pub ahead of print date: 18 April 2013
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Local EPrints ID: 352214
URI: http://eprints.soton.ac.uk/id/eprint/352214
ISSN: 0378-3758
PURE UUID: 5108e660-6756-47a7-a4a4-3962f9f376ea
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Date deposited: 08 May 2013 10:26
Last modified: 14 Mar 2024 13:49
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Author:
Joshua Svenson
Author:
Thomas Santner
Author:
Angela M. Dean
Author:
Hyejung Moon
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