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

2003

Conference Paper

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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.

Author(s): Rasmussen, CE.
Journal: Bayesian Statistics 7
Pages: 651-659
Year: 2003
Day: 0
Editors: J. M. Bernardo, M. J. Bayarri, J. O. Berger, A. P. Dawid, D. Heckerman, A. F. M. Smith and M. West

Department(s): Empirical Inference
Bibtex Type: Conference Paper (inproceedings)

Event Name: Bayesian Statistics 7

Digital: 0
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

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BibTex

@inproceedings{2080,
  title = {Gaussian Processes to Speed up Hybrid Monte Carlo for Expensive Bayesian Integrals},
  author = {Rasmussen, CE.},
  journal = {Bayesian Statistics 7},
  pages = {651-659},
  editors = {J. M. Bernardo, M. J. Bayarri, J. O. Berger, A. P. Dawid, D. Heckerman, A. F. M. Smith and M. West},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  year = {2003}
}