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Bayesian estimation of the covariance function of random fields based on a limited number of measurements

Pieterjan Criel (UGent) , Robby Caspeele (UGent) and Luc Taerwe (UGent)
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Abstract
A Bayesian response surface updating procedure is applied in order to update covariance functions for random fields based on a limited number of measurements. Formulas as well as a numerical algorithm are presented in order to update the parameters of complex response surfaces using Markov Chain Monte Carlo simulations. In case of random fields, the parameters of the covar-iance function are often based on some kind of expert judgment. However, a Bayesian updating technique enables to estimate the parameters of the covari-ance function more rigorously and with less ambiguity. Prior information can be incorporated in the form of vague or informative priors, and the latter can be based on e.g. expert judgment. The proposed estimation procedure is evaluated through numerical simulations and the influence of the position of measurement points is investigated.
Keywords
Bayesian statistics, Markov chain Monte Carlo simulations, random fields, covariance

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Chicago
Criel, Pieterjan, Robby Caspeele, and Luc Taerwe. 2012. “Bayesian Estimation of the Covariance Function of Random Fields Based on a Limited Number of Measurements.” In Proceedings of the 10th International Probabilistic Workshop, ed. Christian Moormann, Maximilian Huber, and Dirk Proske, 19–32. Stuttgart, Germany: DCC Siegmar Kästel.
APA
Criel, Pieterjan, Caspeele, R., & Taerwe, L. (2012). Bayesian estimation of the covariance function of random fields based on a limited number of measurements. In C. Moormann, M. Huber, & D. Proske (Eds.), Proceedings of the 10th international probabilistic workshop (pp. 19–32). Presented at the 10th International Probabilistic Workshop, Stuttgart, Germany: DCC Siegmar Kästel.
Vancouver
1.
Criel P, Caspeele R, Taerwe L. Bayesian estimation of the covariance function of random fields based on a limited number of measurements. In: Moormann C, Huber M, Proske D, editors. Proceedings of the 10th international probabilistic workshop. Stuttgart, Germany: DCC Siegmar Kästel; 2012. p. 19–32.
MLA
Criel, Pieterjan, Robby Caspeele, and Luc Taerwe. “Bayesian Estimation of the Covariance Function of Random Fields Based on a Limited Number of Measurements.” Proceedings of the 10th International Probabilistic Workshop. Ed. Christian Moormann, Maximilian Huber, & Dirk Proske. Stuttgart, Germany: DCC Siegmar Kästel, 2012. 19–32. Print.
@inproceedings{3153747,
  abstract     = {A Bayesian response surface updating procedure is applied in order to update covariance functions for random fields based on a limited number of measurements. Formulas as well as a numerical algorithm are presented in order to update the parameters of complex response surfaces using Markov Chain Monte Carlo simulations. In case of random fields, the parameters of the covar-iance function are often based on some kind of expert judgment. However, a Bayesian updating technique enables to estimate the parameters of the covari-ance function more rigorously and with less ambiguity. Prior information can be incorporated in the form of vague or informative priors, and the latter can be based on e.g. expert judgment. The proposed estimation procedure is evaluated through numerical simulations and the influence of the position of measurement points is investigated.},
  author       = {Criel, Pieterjan and Caspeele, Robby and Taerwe, Luc},
  booktitle    = {Proceedings of the 10th international probabilistic workshop},
  editor       = {Moormann, Christian and Huber, Maximilian and Proske, Dirk},
  isbn         = {9783921837672},
  keyword      = {Bayesian statistics,Markov chain Monte Carlo simulations,random fields,covariance},
  language     = {eng},
  location     = {Stuttgart, Germany},
  pages        = {19--32},
  publisher    = {DCC Siegmar K{\"a}stel},
  title        = {Bayesian estimation of the covariance function of random fields based on a limited number of measurements},
  year         = {2012},
}