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Computer Experiments with Both Quantitative and Qualitative Inputs

Zhang, Yulei
http://rave.ohiolink.edu/etdc/view?acc_num=osu1408042133

Abstract Details

2014, Doctor of Philosophy, Ohio State University, Statistics.
Physical experiments play an important role in agriculture, industry, and medical research. However, physical experiments can sometimes be difficult or even impossible to run. In these situations, computer experiments are becoming desirable surrogates for physical experiments. This dissertation considers designs and the predictive models for computer experiments with both quantitative and qualitative input variables. The existing framework for building Gaussian stochastic process (GaSP) models with quantitative and qualitative inputs is to treat a given set of values of the qualitative inputs as determining a response surface in the qualitative inputs. A GaSP model is assumed for each of these response surfaces and the same covariance structure is used for each response surface. A cross-correlation parameter is introduced for each pair of sets of values of the qualitative variables in order to "capture" correlations between response surfaces. To guarantee that one has a legitimate overall covariance structure, certain conditions are imposed on the cross-correlation parameters. In the first part of this dissertation, we introduce two indicator-based GaSP models by transforming the qualitative inputs into quantitative variables and then use traditional correlation functions for quantitative inputs. We also show the equivalence properties between these new models and the existing model. The second part of this dissertation is about the experimental designs with both quantitative and qualitative inputs. The special data structure requires that a "good" design not only capture the cross-correlation information but also spread observations out over the entire quantitative inputs space. We propose two types of designs, the partial SLHD and partial CSLHD, which are modifications of existing designs in the literature, and compare their prediction accuracy with all the other existing designs for quantitative and qualitative. By examining several examples, we find that what constitutes a "good" design may vary from case to case. We summarize these findings with a "guideline" for selecting initial designs. Furthermore, when the initial design does not perform well, we also propose a sequential design algorithm to interpolate or extrapolate the target response levels in a GaSP model with mixed inputs. Inspired by factor analysis, in the last part of this dissertation, we build a more general composite covariance structure by converting the GaSP model with several qualitative levels into a linear combination of independent stochastic processes with fewer constraints on the variance and correlation functions. Furthermore, this composite covariance structure can be extended to the case with multiple qualitative inputs. In these cases, we introduced the Kronecker product form of the composite covariance function, which can not only reduce the number of the parameters, but also capture the similarity between different qualitative inputs with some identical components. In addition, we propose an ANOVA decomposition form of the Gaussian processes, which imposes a factorial structure on the response outputs. Finally, we extend the sequential design algorithm to the composite GaSP model.
William Notz (Advisor)
Peter Craigmile (Committee Member)
Matthew Pratola (Committee Member)
175 p.
Statistics
Computer Experiments; Physical Experiments; Gaussian Stochastic Process Model; Quantitative and Qualitative Inputs; Cross-Correlation Parameters; Experimental Designs; Composite GaSP Model; Factor Analysis; Kronecker Product; ANOVA Decomposition

Recommended Citations

Citations

  • Zhang, Y. (2014). Computer Experiments with Both Quantitative and Qualitative Inputs [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1408042133

    APA Style (7th edition)

  • Zhang, Yulei. Computer Experiments with Both Quantitative and Qualitative Inputs. 2014. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1408042133.

    MLA Style (8th edition)

  • Zhang, Yulei. "Computer Experiments with Both Quantitative and Qualitative Inputs." Doctoral dissertation, Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1408042133

    Chicago Manual of Style (17th edition)

osu1408042133
614
© 2014, some rights reserved.Creative Commons License Computer Experiments with Both Quantitative and Qualitative Inputs by Yulei Zhang is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by The Ohio State University and OhioLINK.