A monte carlo simulation of the kriging model

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

29 Scopus citations

Abstract

In this paper, we investigate the resulting probability distribution of a kriging model when the values of the model parameters must be estimated from observations of the process being modeled. The output of a kriging model defines a Gaussian probability distribution when the values of the model parameters are given. In practice, these model parameters must be estimated from observations of the process being modeled (typically a computationally expensive computer model). We found that when the model parameters are treated as random variables instead of known values, the resulting probability distribution of the kriging model can be well approximated by a Student-t distribution, a distribution with fatter tails than the Gaussian or normal distribution. The Markov chain Monte Carlo (MCMC) method was used to determine the probability distributions of the model parameters and the output of the kriging model given the observations. The resulting model parameters were validated against the results of a Bayesian analysis of a simple one-dimensional test problem. The results were also compared to the standard method of Maximum Likelihood Estimation as an alternative method to estimate model parameters.

Original languageEnglish (US)
Title of host publicationCollection of Technical Papers - 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference
Pages2039-2053
Number of pages15
StatePublished - Dec 1 2004
EventCollection of Technical Papers - 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference - Albany, NY, United States
Duration: Aug 30 2004Sep 1 2004

Publication series

NameCollection of Technical Papers - 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference
Volume4

Other

OtherCollection of Technical Papers - 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference
CountryUnited States
CityAlbany, NY
Period8/30/049/1/04

All Science Journal Classification (ASJC) codes

  • Engineering(all)

Fingerprint Dive into the research topics of 'A monte carlo simulation of the kriging model'. Together they form a unique fingerprint.

Cite this