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Annealed Adaptive Slice Sampling for Gaussian Process HyperParameter
Estimation
A. GarbunoIñigo, F.A. DiazDelaO, and K.M. Zuev
International Journal for Uncertainty Quantification,
vol. 6, no. 4, pp. 341359, Sep. 2016.
[Web DOI
 Paper pdf  arXiv stat.CO
1509.00349]
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 underlyig hyperparameters
are estimated via gradientfree optimisation or genetic algorithms,
to name a few methods. On the other hand, maximum a posteriori
(MAP) estimation could discard important regions of the hyperparameter
space. In this paper, we carry out a more complete Bayesian
inference, through combining Slice Sampling with some recently
developed Sequential Monte Carlo samplers. The resulting algorithm
improves the mixing in the sampling through delayedrejection,
the inclusion of an annealing scheme akin to Asymptotically
Independent Markov Sampling and parallelisation via Trainsitional
Markov Chain Monte Carlo. Examples related to the estimation
of hyperparameters, as well as examples applied in other contexts
of Bayesian inference, 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 this
http URL. 

