On the Bayesian Treed Multivariate Gaussian Process with Linear Model of Coregionalization

Konomi, Bledar A.; Karagiannis, Georgios; Lin, Guang

doi:10.1016/j.jspi.2014.08.010

Title: On the Bayesian Treed Multivariate Gaussian Process with Linear Model of Coregionalization

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Abstract

The Bayesian treed Gaussian process (BTGP) has gained popularity in recent years because it provides a straightforward mechanism for modeling non-stationary data and can alleviate computational demands by fitting models to less data. The extension of BTGP to the multivariate setting requires us to model the cross-covariance and to propose efficient algorithms that can deal with trans-dimensional MCMC moves. In this paper we extend the cross-covariance of the Bayesian treed multivariate Gaussian process (BTMGP) to that of linear model of Coregionalization (LMC) cross-covariances. Different strategies have been developed to improve the MCMC mixing and invert smaller matrices in the Bayesian inference. Moreover, we compare the proposed BTMGP with existing multiple BTGP and BTMGP in test cases and multiphase flow computer experiment in a full scale regenerator of a carbon capture unit. The use of the BTMGP with LMC cross-covariance helped to predict the computer experiments relatively better than existing competitors. The proposed model has a wide variety of applications, such as computer experiments and environmental data. In the case of computer experiments we also develop an adaptive sampling strategy for the BTMGP with LMC cross-covariance function.

Authors:: Konomi, Bledar A.; Karagiannis, Georgios; Lin, Guang

Publication Date:: Sun Feb 01 00:00:00 EST 2015

Research Org.:: Pacific Northwest National Lab. (PNNL), Richland, WA (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1184929

Report Number(s):: PNNL-SA-96827
AA9010100

DOE Contract Number:: AC05-76RL01830

Resource Type:: Journal Article

Journal Name:: Computational Statistics & Data Analysis, 157-58:1-15

Additional Journal Information:: Journal Name: Computational Statistics & Data Analysis, 157-58:1-15

Country of Publication:: United States

Language:: English

Citation Formats


                    Konomi, Bledar A., Karagiannis, Georgios, and Lin, Guang. On the Bayesian Treed Multivariate Gaussian Process with Linear Model of Coregionalization.  United States: N. p., 2015. 
        Web.  doi:10.1016/j.jspi.2014.08.010.

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                    Konomi, Bledar A., Karagiannis, Georgios, & Lin, Guang. On the Bayesian Treed Multivariate Gaussian Process with Linear Model of Coregionalization.  United States.  https://doi.org/10.1016/j.jspi.2014.08.010

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                    Konomi, Bledar A., Karagiannis, Georgios, and Lin, Guang. 2015.  
        "On the Bayesian Treed Multivariate Gaussian Process with Linear Model of Coregionalization".  United States.  https://doi.org/10.1016/j.jspi.2014.08.010.

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@article{osti_1184929,

  title        = {On the Bayesian Treed Multivariate Gaussian Process with Linear Model of Coregionalization},

  author       = {Konomi, Bledar A. and Karagiannis, Georgios and Lin, Guang},

  abstractNote = {The Bayesian treed Gaussian process (BTGP) has gained popularity in recent years because it provides a straightforward mechanism for modeling non-stationary data and can alleviate computational demands by fitting models to less data. The extension of BTGP to the multivariate setting requires us to model the cross-covariance and to propose efficient algorithms that can deal with trans-dimensional MCMC moves. In this paper we extend the cross-covariance of the Bayesian treed multivariate Gaussian process (BTMGP) to that of linear model of Coregionalization (LMC) cross-covariances. Different strategies have been developed to improve the MCMC mixing and invert smaller matrices in the Bayesian inference. Moreover, we compare the proposed BTMGP with existing multiple BTGP and BTMGP in test cases and multiphase flow computer experiment in a full scale regenerator of a carbon capture unit. The use of the BTMGP with LMC cross-covariance helped to predict the computer experiments relatively better than existing competitors. The proposed model has a wide variety of applications, such as computer experiments and environmental data. In the case of computer experiments we also develop an adaptive sampling strategy for the BTMGP with LMC cross-covariance function.},

  doi          = {10.1016/j.jspi.2014.08.010},

  url          = {https://www.osti.gov/biblio/1184929},
  journal      = {Computational Statistics & Data Analysis, 157-58:1-15},
number       = ,

  volume       = ,

  place        = {United States},

  year         = {Sun Feb 01 00:00:00 EST 2015},

  month        = {Sun Feb 01 00:00:00 EST 2015}

}

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