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Gaussian process hyper-parameter estimation using Parallel Asymptotically Independent Markov Sampling

Garbuno-Inigo, A. and DiazDelaO, F. A. and Zuev, K. M. (2016) Gaussian process hyper-parameter estimation using Parallel Asymptotically Independent Markov Sampling. Computational Statistics and Data Analysis, 103 . pp. 367-383. ISSN 0167-9473. doi:10.1016/j.csda.2016.05.019.

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Gaussian process emulators of computationally expensive computer codes provide fast statistical approximations to model physical processes. The training of these surrogates depends on the set of design points chosen to run the simulator. Due to computational cost, such training set is bound to be limited and quantifying the resulting uncertainty in the hyper-parameters of the emulator by uni-modal distributions is likely to induce bias. In order to quantify this uncertainty, this paper proposes a computationally efficient sampler based on an extension of Asymptotically Independent Markov Sampling, a recently developed algorithm for Bayesian inference. Structural uncertainty of the emulator is obtained as a by-product of the Bayesian treatment of the hyper-parameters. Additionally, the user can choose to perform stochastic optimisation to sample from a neighbourhood of the Maximum a Posteriori estimate, even in the presence of multimodality. Model uncertainty is also acknowledged through numerical stabilisation measures by including a nugget term in the formulation of the probability model. The efficiency of the proposed sampler is illustrated in examples where multi-modal distributions are encountered. For the purpose of reproducibility, further development, and use in other applications the code used to generate the examples is freely available for download at

Item Type:Article
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URLURL TypeDescription
Garbuno-Inigo, A.0000-0003-3279-619X
Zuev, K. M.0000-0003-2174-700X
Additional Information:© 2016 Elsevier B.V. Received 25 June 2015, Revised 3 December 2015, Accepted 29 May 2016, Available online 6 June 2016. The first author gratefully acknowledges the Consejo Nacional de Ciencia y Tecnología (CONACYT) (Grant number: 381321) for the award of a scholarship from the Mexican government.
Funding AgencyGrant Number
Consejo Nacional de Ciencia y Tecnología (CONACYT)381321
Subject Keywords:Gaussian process; Hyper-parameter; Marginalisation; Optimisation; MCMC; Simulated annealing
Record Number:CaltechAUTHORS:20160915-102817468
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Official Citation:A. Garbuno-Inigo, F.A. DiazDelaO, K.M. Zuev, Gaussian process hyper-parameter estimation using Parallel Asymptotically Independent Markov Sampling, Computational Statistics & Data Analysis, Volume 103, November 2016, Pages 367-383, ISSN 0167-9473,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:70371
Deposited By: Tony Diaz
Deposited On:28 Sep 2016 17:14
Last Modified:04 Apr 2022 19:03

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