Transitional annealed adaptive slice sampling for Gaussian process hyper-parameter estimation
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.
Additional Information
© 2016 Begell House Inc. The first author gratefully acknowledges the Consejo Nacional de Ciencia y Tecnología (CONACyT) for the award of a scholarship from the Mexican government for graduate studies. The authors would like to thank additionally an anonymous reviewer for his/her comments to improve the quality of this paper.Attached Files
Submitted - 1509.00349.pdf
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Additional details
- Eprint ID
- 72513
- Resolver ID
- CaltechAUTHORS:20161202-081658334
- Consejo Nacional de Ciencia y Tecnología (CONACyT)
- Created
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2016-12-02Created from EPrint's datestamp field
- Updated
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2022-03-23Created from EPrint's last_modified field