A Bayesian metamodeling approach for stochastic simulations

Yin, Jun; Ng, Szu Hui; Ng, Kien Ming

doi:10.1109/wsc.2010.5679086

“…We sometimes refer to M(x) and ε j (x) as the extrinsic and intrinsic uncertainties, respectively, at design point x, as they were defined in Ankenman et al [2010]. Yin et al [2010] also propose an extension of kriging to stochastic simulation. Their metamodel is similar to Eq.…”

Section: Stochastic Krigingmentioning

confidence: 99%

The effects of common random numbers on stochastic kriging metamodels

Chen¹,

Ankenman²,

Nelson³

2012

ACM Trans. Model. Comput. Simul.

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Ankenman et al. introduced stochastic kriging as a metamodeling tool for representing stochastic simulation response surfaces, and employed a very simple example to suggest that the use of Common Random Numbers (CRN) degrades the capability of stochastic kriging to predict the true response surface. In this article we undertake an in-depth analysis of the interaction between CRN and stochastic kriging by analyzing a richer collection of models; in particular, we consider stochastic kriging models with a linear trend term. We also perform an empirical study of the effect of CRN on stochastic kriging. We also consider the effect of CRN on metamodel parameter estimation and response-surface gradient estimation, as well as response-surface prediction. In brief, we confirm that CRN is detrimental to prediction, but show that it leads to better estimation of slope parameters and superior gradient estimation compared to independent simulation.

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“…An alternative method is used in [21], to examine the consequences of estimating σ 2 and θ (through MLE); i.e., that article uses a first-order expansion of the MSE; earlier, Abt [1] also used first-order Taylor series expansion. One more alternative method developed in [32] uses the Bayesian approach. Our specific bootstrapped estimator is simpler.…”

Section: Kriging Metamodelsmentioning

confidence: 99%

“…141-153] discusses numerical noise, not noise caused by pseudorandom numbers (which are used in discrete-event simulation). For the latter noise we refer to [2], [23], and [32].…”

Section: Hartmann-6 Functionmentioning

confidence: 99%

Expected Improvement in Efficient Global Optimization Through Bootstrapped Kriging

Kleijnen

¹

,

Beers

²

,

Nieuwenhuyse

³

2011

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This article uses a sequentialized experimental design to select simulation input combinations for global optimization, based on Kriging (also called Gaussian process or spatial correlation modeling); this Kriging is used to analyze the input/output data of the simulation model (computer code). This design and analysis adapt the classic "expected improvement" (EI) in "efficient global optimization" (EGO) through the introduction of an improved estimator of the Kriging predictor variance; this estimator uses parametric bootstrapping. Classic EI and bootstrapped EI are compared through various test functions, including the six-hump camel-back and several Hartmann functions. These empirical results demonstrate that in some applications bootstrapped EI finds the global optimum faster than classic EI does; in general, however, the classic EI may be considered to be a robust global optimizer.

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“…An alternative method is used in [21], to examine the consequences of estimating σ 2 and θ (through MLE); i.e., that article uses a first-order expansion of the MSE; earlier, Abt [1] also used first-order Taylor series expansion. One more alternative method developed in [32] uses the Bayesian approach. Our specific bootstrapped estimator is simpler.…”

Section: Kriging Metamodelsmentioning

confidence: 99%

“…141-153] discusses numerical noise, not noise caused by pseudorandom numbers (which are used in discrete-event simulation). For the latter noise we refer to [2], [23], and [32]. • Application to large-scale industrial problems, such as the so-called MOPTA08 problem with 124 inputs and 68 inequality constraints for the outputs; see [24] • Comparison of EGO with other approaches; see [5].…”

Section: Conclusion and Future Researchmentioning

confidence: 99%

Expected improvement in efficient global optimization through bootstrapped kriging

Kleijnen

¹

,

Beers

²

,

Nieuwenhuyse

³

2011

View full text Add to dashboard Cite

This article uses a sequentialized experimental design to select simulation input combinations for global optimization, based on Kriging (also called Gaussian process or spatial correlation modeling); this Kriging is used to analyze the input/output data of the simulation model (computer code). This design and analysis adapt the classic "expected improvement" (EI) in "efficient global optimization" (EGO) through the introduction of an improved estimator of the Kriging predictor variance; this estimator uses parametric bootstrapping. Classic EI and bootstrapped EI are compared through various test functions, including the six-hump camel-back and several Hartmann functions. These empirical results demonstrate that in some applications bootstrapped EI finds the global optimum faster than classic EI does; in general, however, the classic EI may be considered to be a robust global optimizer. Keywords Simulation • Optimization • Kriging • Bootstrap 1 Introduction Simulation is often used to estimate the global optimum of the real system being simulated (like many researchers in this area do, we use the terms "optimum" and "optimization" even

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A Bayesian metamodeling approach for stochastic simulations

Cited by 6 publications

References 18 publications

The effects of common random numbers on stochastic kriging metamodels

The effects of common random numbers on stochastic kriging metamodels

Expected Improvement in Efficient Global Optimization Through Bootstrapped Kriging

Expected improvement in efficient global optimization through bootstrapped kriging

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