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Bayesian Statistics 9$
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José M. Bernardo, M. J. Bayarri, James O. Berger, A. P. Dawid, David Heckerman, Adrian F. M. Smith, and Mike West

Print publication date: 2011

Print ISBN-13: 9780199694587

Published to Oxford Scholarship Online: January 2012

DOI: 10.1093/acprof:oso/9780199694587.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 13 April 2021

Using TPA for Bayesian Inference *

Using TPA for Bayesian Inference *

(p.257) Using TPA for Bayesian Inference*
Bayesian Statistics 9

Mark Huber

Sarah Schott

Oxford University Press

Finding the integrated likelihood of a model given the data requires the integration of a nonnegative function over the parameter space. Classical Monte Carlo methods for numerical integration require a bound or estimate of the variance in order to determine the quality of the output. The method called the product estimator does not require knowledge of the variance in order to produce a result of guaranteed quality, but requires a cooling schedule that must have certain strict properties. Finding a cooling schedule can be difficult, and finding an optimal cooling schedule is usually computationally out of reach. TPA is a method that solves this difficulty, creating an optimal cooling schedule automatically as it is run. This method has its own set of requirements; here it is shown how to meet these requirements for problems arising in Bayesian inference. This gives guaranteed accuracy for integrated likelihoods and posterior means of nonnegative parameters.

Keywords:   Adaptive Monte Carlo, Variance Free Approximation

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