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  Gaussian Processes to Speed up Hybrid Monte Carlo for Expensive Bayesian Integrals

Rasmussen, C. (2003). Gaussian Processes to Speed up Hybrid Monte Carlo for Expensive Bayesian Integrals. In J. Bernardo, J. Bayarri, J. Berger, A. Dawid, D. Heckerman, A. Smith, et al. (Eds.), Bayesian Statistics 7 (pp. 651-659). Oxford, UK: Oxford University Press.

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Rasmussen, CE1, Author              
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 Abstract: Hybrid Monte Carlo (HMC) is often the method of choice for computing Bayesian integrals that are not analytically tractable. However the success of this method may require a very large number of evaluations of the (un-normalized) posterior and its partial derivatives. In situations where the posterior is computationally costly to evaluate, this may lead to an unacceptable computational load for HMC. I propose to use a Gaussian Process model of the (log of the) posterior for most of the computations required by HMC. Within this scheme only occasional evaluation of the actual posterior is required to guarantee that the samples generated have exactly the desired distribution, even if the GP model is somewhat inaccurate. The method is demonstrated on a 10 dimensional problem, where 200 evaluations suffice for the generation of 100 roughly independent points from the posterior. Thus, the proposed scheme allows Bayesian treatment of models with posteriors that are computationally demanding, such as models involving computer simulation.

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 Dates: 2003
 Publication Status: Published in print
 Pages: -
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 Rev. Type: -
 Identifiers: BibTex Citekey: 2080
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Title: Seventh Valencia international meeting, dedicated to Dennis V. Lindley
Place of Event: Arona, Spain
Start-/End Date: 2002-06-02 - 2002-06-06

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Title: Bayesian Statistics 7
Source Genre: Proceedings
 Creator(s):
Bernardo, JM, Editor
Bayarri, JM, Editor
Berger, JO, Editor
Dawid, AP, Editor
Heckerman, D, Editor
Smith, AFM, Editor
West, M, Editor
Affiliations:
-
Publ. Info: Oxford, UK : Oxford University Press
Pages: 750 Volume / Issue: - Sequence Number: - Start / End Page: 651 - 659 Identifier: ISBN: 0-19-852615-6