Generalized Integrated Brownian Fields for Simulation Metamodeling

Salemi, Peter and Staum, Jeremy and Nelson, Barry (2019) Generalized Integrated Brownian Fields for Simulation Metamodeling. Operations Research, 67 (3). pp. 874-891. ISSN 0030-364X

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We introduce a novel class of Gaussian random fields (GRFs), called generalized integrated Brownian fields (GIBFs), focusing on the use of GIBFs for Gaussian process regression in deterministic and stochastic simulation metamodeling. We build GIBFs from the well-known Brownian motion and discuss several of their properties, including differentiability that cart differ in each coordinate, no mean reversion, and the Markov property. We explain why we desire to use GRFs with these properties and provide formal definitions of mean reversion and the Markov property for real-valued, differentiable random fields. We show how to use GIBFs with stochastic kriging, covering trend modeling and parameter fitting, discuss their approximation capability, and show that the resulting metamodel also has differentiability that can differ in each coordinate. Last, we use several examples to demonstrate superior prediction capability as compared with the GRFs corresponding to the Gaussian and Matern covariance functions.

Item Type:
Journal Article
Journal or Publication Title:
Operations Research
Additional Information:
Copyright 2019 INFORMS
Uncontrolled Keywords:
?? simulation metamodelinggaussian random fieldskrigingstochastic kriginggaussian process regressionmean reversionmarkov propertymanagement science and operations researchcomputer science applications ??
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Deposited On:
11 Mar 2020 10:10
Last Modified:
07 Nov 2023 01:03