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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.