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

Garbuno Inigo, A, DiazDeLaO, FA and Zuev, KM (2016) Gaussian process hyper-parameter estimation using Parallel Asymptotically Independent Markov Sampling. Computational Statistics & Data Analysis, 103. pp. 367-383.

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Abstract

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 https://github.com/agarbuno/paims_codes.

Item Type:	Article
Additional Information:	Computational Statistics \& Data Analysis, Volume 103, November 2016
Uncontrolled Keywords:	Gaussian process, Hyper-parameter, Marginalisation, Optimisation, MCMC, Simulated annealing
Subjects:	?? QA ??
Depositing User:	Symplectic Admin
Date Deposited:	04 Apr 2017 09:05
Last Modified:	19 Jan 2023 07:07
DOI:	10.1016/j.csda.2016.05.019
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3006780

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• Gaussian process hyper-parameter estimation using Parallel Asymptotically Independent Markov Sampling. (deposited 27 Oct 2015 09:02)
  • Gaussian process hyper-parameter estimation using Parallel Asymptotically Independent Markov Sampling. (deposited 04 Apr 2017 09:05) [Currently Displayed]