A numerical study of the effects of the parameterization of the gaussian process
department or school: Arts and Sciences, Irving K. Barber School of (Okanagan)
department or school: Computer Science, Mathematics, Physics and Statistics, Department of (Okanagan)
data provider: DSpace
degree campus: UBCO
creator: Foster, Jodie Lynn
issued: 2017-07-31T23:08:08Z
issued: 2017
related degree: Master of Science - MSc
degree grantor: University of British Columbia
description: Mathematical models implemented as computer code are gaining widespread use across the sciences and engineering. In some cases these model are even replacing physical experiments. The computational complexity of the models typically limits the number of runs that can be performed. In such cases, the Gaussian process is used to emulate the true computer model so that experiments are performed on the emulator. The applicability of the emulator is closely related to the quality of the fitted Gaussian process model. A key step in fitting the Gaussian process is estimating the unknown correlation parameters using a numerical optimizer. It is well known that maximum likelihood estimation is invariant to the parameterization of the model. When the mapping from one parametrization to another is injective this leads to an equivalence of the likelihood and in a Bayesian context an equivalence of the posterior for carefully chosen prior distributions. In the context of a Gaussian process model, we show that the parameterization of the model is in fact critical to achieving meaningful results and ensuring convergence of the optimizer. This thesis is aimed at providing practical advice on the best parameterization for the Gaussian process model. The approach presented here implements a simulation study on a wide range of test problems and a large number of parameterizations. We illustrate that the parameterization can have a huge effect on the fitted model and show that many of the commonly used parameterizations are in fact sub-optimal for fitting the Gaussian process.
aggregated CHO: https://circle.library.ubc.ca/rest/handle/2429/62463
note: A Numerical Study of the Effects ofthe Parameterization of the GaussianProcessbyJodie Lynn FosterB.Sc., The University of British Columbia, 2013A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinThe College of Graduate Studies(Computer Science)THE UNIVERSITY OF BRITISH COLUMBIA(Okanagan)August 2017© Jodie Lynn Foster, 2017The undersigned certify that they have read, and recommend to theCollege of Graduate Studies for acceptance, a thesis entitled: A NumericalStudy of the Effects of the Parameterization of the GaussianProcess submitted by Jodie Lynn Foster in partial fulfilment of therequirements of the degree of Master of ScienceJason Loeppky, Irving K. Barber School of Arts and SciencesSupervisor, ProfessorJohn Braun, Irving K. Barber School of Arts and SciencesSupervisory Committee Member, ProfessorParamjit Gill, Irving K. Barber School of Arts and SciencesSupervisory Committee Member, ProfessorJulian Cheng, School of EngineeringUniversity Examiner, ProfessorJuly 31, 2017(Date Submitted to Grad Studies)iiAbstractMathematical models implemented as computer code are gaining widespreaduse across the sciences and engineering. In some cases these model areeven replacing physical experiments. The computational complexity of themodels typically limits the number of runs that can be performed. In suchcases, the Gaussian process is used to emulate the true computer modelso that experiments are performed on the emulator. The applicability ofthe emulator is closely related to the quality of the fitted Gaussian processmodel. A key step in fitting the Gaussian process is estimating the unknowncorrelation parameters using a numerical optimizer. It is well known thatmaximum likelihood estimation is invariant to the parameterization of themodel. When the mapping from one parametrization to another is injectivethis leads to an equivalence of the likelihood and in a Bayesian context anequivalence of the posterior for carefully chosen pr…
has type: Thesis/Dissertation
date issued: 2017-09
is shown at: 10.14288/1.0349139
language: eng
degree discipline: Computer Science
provider: Vancouver : University of British Columbia Library
publisher: University of British Columbia
rights: Attribution-NoDerivatives 4.0 International
rights URI: http://creativecommons.org/licenses/by-nd/4.0/
scholar level: Graduate
type: Text
identifier URI: http://hdl.handle.net/2429/62463