Using maximum likelihood estimation to estimate kriging model parameters

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

A kriging model can be used as a surrogate to a more computationally expensive model or simulation. It is capable of providing a continuous mathematical relationship that can interpolate a set of observations. One of the major issues with using kriging models is the potentially computationally expensive process of estimating the best model parameters. One of the most common methods used to estimate model parameters is Maximum Likelihood Estimation (MLE). MLE of kriging model parameters requires the use of numerical optimization of a continuous but possibly multi-modal log-likelihood function. This paper presents some enhancements to gradient-based methods to make them more computationally efficient and compares the potential reduction in computational burden. These enhancements include the development of the analytic gradient and Hessian for the loglikelihood equation of a kriging model that uses a Gaussian spatial correlation function. The suggested algorithm is very similar to the Scoring algorithm traditionally used in statistics, a Newton-Raphson gradient-based optimization method.

Original languageEnglish (US)
Title of host publication2007 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2007
Pages663-673
Number of pages11
DOIs
StatePublished - Jun 17 2008
Event33rd Design Automation Conference, presented at - 2007 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2007 - Las Vegas, NV, United States
Duration: Sep 4 2007Sep 7 2007

Publication series

Name2007 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2007
Volume6 PART A

Other

Other33rd Design Automation Conference, presented at - 2007 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2007
CountryUnited States
CityLas Vegas, NV
Period9/4/079/7/07

All Science Journal Classification (ASJC) codes

  • Computer Graphics and Computer-Aided Design
  • Computer Science Applications
  • Mechanical Engineering
  • Modeling and Simulation

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    Martin, J. D. (2008). Using maximum likelihood estimation to estimate kriging model parameters. In 2007 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2007 (pp. 663-673). (2007 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2007; Vol. 6 PART A). https://doi.org/10.1115/DETC2007-34662