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GPfit: An R Package for Fitting a Gaussian Process Model to Deterministic Simulator Outputs

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  • MacDonald, Blake
  • Ranjan, Pritam
  • Chipman, Hugh

Abstract

Gaussian process (GP) models are commonly used statistical metamodels for emulating expensive computer simulators. Fitting a GP model can be numerically unstable if any pair of design points in the input space are close together. Ranjan, Haynes, and Karsten (2011) proposed a computationally stable approach for fitting GP models to deterministic computer simulators. They used a genetic algorithm based approach that is robust but computationally intensive for maximizing the likelihood. This paper implements a slightly modified version ofthe model proposed by Ranjan et al. (2011 ) in the R package GPfit. A novel parameterization of the spatial correlation function and a clustering based multi-start gradient based optimization algorithm yield robust optimization that is typically faster than the genetic algorithm based approach. We present two examples with R codes to illustrate the usage of the main functions in GPfit . Several test functions are used for performance comparison with the popular R package mlegp . We also use GPfit for a real application, i.e., for emulating the tidal kinetic energy model for the Bay of Fundy, Nova Scotia, Canada. GPfit is free software and distributed under the General Public License and available from the Comprehensive R Archive Network.

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  • MacDonald, Blake & Ranjan, Pritam & Chipman, Hugh, 2015. "GPfit: An R Package for Fitting a Gaussian Process Model to Deterministic Simulator Outputs," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 64(i12).
    • Handle: RePEc:jss:jstsof:v:064:i12
    DOI: http://hdl.handle.net/10.18637/jss.v064.i12
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    References listed on IDEAS

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    1. Zeileis, Achim & Hornik, Kurt & Murrell, Paul, 2009. "Escaping RGBland: Selecting colors for statistical graphics," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3259-3270, July.
    2. Gramacy, Robert B & Lee, Herbert K. H, 2008. "Bayesian Treed Gaussian Process Models With an Application to Computer Modeling," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1119-1130.
    3. Gramacy, Robert B., 2007. "tgp: An R Package for Bayesian Nonstationary, Semiparametric Nonlinear Regression and Design by Treed Gaussian Process Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 19(i09).
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    2. Palomo, Jesús & Paulo, Rui & García-Donato, Gonzalo, 2015. "SAVE: An R Package for the Statistical Analysis of Computer Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 64(i13).
    3. Oskar Gustafsson & Mattias Villani & Pär Stockhammar, 2023. "Bayesian optimization of hyperparameters from noisy marginal likelihood estimates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(4), pages 577-595, June.
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    5. Erickson, Collin B. & Ankenman, Bruce E. & Sanchez, Susan M., 2018. "Comparison of Gaussian process modeling software," European Journal of Operational Research, Elsevier, vol. 266(1), pages 179-192.
    6. Steven Wilkins Reeves & Shane Lubold & Arun G. Chandrasekhar & Tyler H. McCormick, 2024. "Model-Based Inference and Experimental Design for Interference Using Partial Network Data," Papers 2406.11940, arXiv.org.

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