Rights statement: Copyright 2019 INFORMS
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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Generalized Integrated Brownian Fields for Simulation Metamodeling
AU - Salemi, Peter
AU - Staum, Jeremy
AU - Nelson, Barry
N1 - Copyright 2019 INFORMS
PY - 2019/6/10
Y1 - 2019/6/10
N2 - 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.
AB - 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.
KW - simulation metamodeling
KW - Gaussian random fields
KW - kriging
KW - stochastic kriging
KW - Gaussian process regression
KW - mean reversion
KW - Markov property
U2 - 10.1287/opre.2018.1804
DO - 10.1287/opre.2018.1804
M3 - Journal article
VL - 67
SP - 874
EP - 891
JO - Operations Research
JF - Operations Research
SN - 0030-364X
IS - 3
ER -