Gaussian Process Models for Computer Experiments With Qualitative and Quantitative Factors

Qian, Peter Z. G.; Wu, Huaiqing; Wu, Changbao

doi:10.1198/004017008000000262

Cited by 207 publications

(186 citation statements)

References 12 publications

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“…This section describes a computationally efficient method developed in Zhou, Qian, and Zhou [34] for fitting Gaussian process models with quantitative and qualitative factors proposed in Qian, Wu, and Wu [17]. Consider a computer model with inputs w = (x t , z t ) t , where x = (x 1 , .…”

Section: Gaussian Processes For Models With Quantitative and Qualitatmentioning

confidence: 99%

“…Typically, the covariance function is a function of the distance between the points. Qian et al have studied a variety of covariance functions that represent the covariance between discrete points [17][34]. They provide several correlation functions that are appropriate to use for mixed variable problems: we investigated the exchangeable correlation (EC), the multiplicative correlation (MC), and the unrestricted correlation function (UC).…”

Section: Chapter 2 Mixed Surrogate Approachesmentioning

confidence: 99%

“…Gaussian process models with ordinal qualitative factors can be found in Section 4.4 of [17]. The response of the computer model at an input value w is modeled as…”

Section: Gaussian Processes For Models With Quantitative and Qualitatmentioning

confidence: 99%

“…This condition can be achieved in two ways. One way is to use the semi-definite programming techniques with positive definiteness constraints [17], which are computationally intensive. [34] provides a more efficient way for modeling T by using the hypersphere decomposition, originally introduced for modeling correlations in financial applications [18].…”

Section: Gaussian Processes For Models With Quantitative and Qualitatmentioning

confidence: 99%

See 3 more Smart Citations

Surrogate Models for Mixed Discrete-Continuous Variables

Swiler

Hough

Qian

et al. 2014

Constraint Programming and Decision Making

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3Abstract Large-scale computational models have become common tools for analyzing complex manmade systems. However, when coupled with optimization or uncertainty quantification methods in order to conduct extensive model exploration and analysis, the computational expense quickly becomes intractable. Furthermore, these models may have both continuous and discrete parameters. One common approach to mitigating the computational expense is the use of response surface approximations. While well developed for models with continuous parameters, they are still new and largely untested for models with both continuous and discrete parameters. In this work, we describe and investigate the performance of three types of response surfaces developed for mixedvariable models: Adaptive Component Selection and Shrinkage Operator, Treed Gaussian Process, and Gaussian Process with Special Correlation Functions. We focus our efforts on test problems with a small number of parameters of interest, a characteristic of many physics-based engineering models. We present the results of our studies and offer some insights regarding the performance of each response surface approximation method. 4 AcknowledgmentsWe thank the Laboratory Directed Research and Development (LDRD) team for many fruitful discussions on this topic and the ongoing support of this project. The LDRD team and associated colleagues includes:

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Section: Gaussian Processes For Models With Quantitative and Qualitatmentioning

confidence: 99%

Section: Chapter 2 Mixed Surrogate Approachesmentioning

confidence: 99%

“…Gaussian process models with ordinal qualitative factors can be found in Section 4.4 of [17]. The response of the computer model at an input value w is modeled as…”

Section: Gaussian Processes For Models With Quantitative and Qualitatmentioning

confidence: 99%

Section: Gaussian Processes For Models With Quantitative and Qualitatmentioning

confidence: 99%

See 2 more Smart Citations

Surrogate Models for Mixed Discrete-Continuous Variables

Swiler

Hough

Qian

et al. 2014

Constraint Programming and Decision Making

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show abstract

“…Equation (1) is a weighted sum (with respect to β > 0) of the L 2 distance for quantitative variables and the 0-1 distance for qualitative variables. Such distance measures were defined and applied to Gaussian process models by Qian et al (2008). Let ζ = {x 1 , .…”

Section: Coverage and Spread Designsmentioning

confidence: 99%

Weighted space-filling designs

Bowman

Woods

2013

Journal of Simulation

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Many computer models or simulators have probabilistic dependencies between their input variables, which if not accounted for during design selection may result in a large numbers of simulator runs being required for analysis. We propose a method which incorporates known dependencies between input variables into design selection for simulators and demonstrate the benefits of this approach via a simulator for atmospheric dispersion. We quantify the benefit of the new techniques over standard space-filling and Monte Carlo simulation. The proposed methods are adaptations of computer-generated spread and coverage space-filling designs, with "distance" between two input points redefined to include a weight function. This weight function reflects any known multivariate dependencies between input variables and prior information on the design region. The methods can include quantitative and qualitative variables, and different types of prior information. Novel graphical methods, adapted from fraction of design space plots, are used to assess and compare the designs.

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Sensitivity Analysis of Computer Models

Fassò

2015

Wiley StatsRef: Statistics Reference Online

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Sensitivity analysis (SA) of computer models has been developed over the last decades paralleling the development of massive computer simulations of engineering, chemical, and environmental systems. Through extensive simulations, global SA is aimed at assessing the importance of each input to the model outputs by means of variance decomposition. Depending on model complexity and simulation costs, various techniques are available ranging from design of experiments (DOE) to intensive Monte Carlo, metamodeling, and inference.

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Gaussian Process Models for Computer Experiments With Qualitative and Quantitative Factors

Cited by 207 publications

References 12 publications

Surrogate Models for Mixed Discrete-Continuous Variables

Surrogate Models for Mixed Discrete-Continuous Variables

Weighted space-filling designs

Sensitivity Analysis of Computer Models

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