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Estimating Ratios of Normalizing Constants

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Monte Carlo Methods in Bayesian Computation

Part of the book series: Springer Series in Statistics ((SSS))

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Abstract

A computational problem arising frequently in Bayesian inference is the computation of normalizing constants for posterior densities from which we can sample. Typically, we are interested in the ratios of such normalizing constants. For example, a Bayes factor is defined as the ratio of posterior odds versus prior odds, where posterior odds is simply a ratio of the normalizing constants of two posterior densities. Mathematically, this problem can be formulated as follows. Let πl (θ), l = 1,2, be two densities, each of which is known up to a normalizing constant:

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© 2000 Springer Science+Business Media New York

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Chen, MH., Shao, QM., Ibrahim, J.G. (2000). Estimating Ratios of Normalizing Constants. In: Monte Carlo Methods in Bayesian Computation. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1276-8_5

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  • DOI: https://doi.org/10.1007/978-1-4612-1276-8_5

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7074-4

  • Online ISBN: 978-1-4612-1276-8

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