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International Journal for Uncertainty Quantification

Impact factor: 1.000

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2016018590
pages 341-359

TRANSITIONAL ANNEALED ADAPTIVE SLICE SAMPLING FOR GAUSSIAN PROCESS HYPER-PARAMETER ESTIMATION

Alfredo Garbuno-Inigo
Institute for Risk and Uncertainty, School of Engineering, University of Liverpool, Brownlow Hill, Liverpool, L69 3GH, United Kingdom
F. A. DiazDelaO
Institute for Risk and Uncertainty, School of Engineering, University of Liverpool, Brownlow Hill, Liverpool, L69 3GH, United Kingdom
Konstantin M. Zuev
Department of Computing and Mathematical Sciences, Division of Engineering and Applied Science, 1200 E California Blvd., California Institute of Technology, Pasadena, California 91125, USA

ABSTRACT

Surrogate models have become ubiquitous in science and engineering for their capability of emulating expensive computer codes, necessary to model and investigate complex phenomena. Bayesian emulators based on Gaussian processes adequately quantify the uncertainty that results from the cost of the original simulator, and thus the inability to evaluate it on the whole input space. However, it is common in the literature that only a partial Bayesian analysis is carried out, whereby the underlying hyper-parameters are estimated via gradient-free optimization or genetic algorithms, to name a few methods. On the other hand, maximum a posteriori (MAP) estimation could discard important regions of the hyper-parameter space. In this paper, we carry out a more complete Bayesian inference, that combines Slice Sampling with some recently developed sequential Monte Carlo samplers. The resulting algorithm improves the mixing in the sampling through the delayed-rejection nature of Slice Sampling, the inclusion of an annealing scheme akin to Asymptotically Independent Markov Sampling and parallelization via transitional Markov chain Monte Carlo. Examples related to the estimation of Gaussian process hyper-parameters are presented. For the purpose of reproducibility, further development, and use in other applications, the code to generate the examples in this paper is freely available for download at http://github.com/agarbuno/ta2s2_codes.