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  • Neal_Kypraios_2014

    Rights statement: © The Author(s) 2013. This article is published with open access at Springerlink.com

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Exact Bayesian inference via data augmentation

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<mark>Journal publication date</mark>03/2015
<mark>Journal</mark>Statistics and Computing
Issue number2
Volume25
Number of pages15
Pages (from-to)333-347
Publication statusPublished
Early online date3/12/13
Original languageEnglish

Abstract

Data augmentation is a common tool in Bayesian statistics, especially in the application of MCMC. Data augmentation is used where direct computation of the posterior density, π(θ|x), of the parameters θ, given the observed data x, is not possible. We show that for a range of problems, it is possible to augment the data by y, such that, π(θ|x,y) is known, and π(y|x) can easily be computed. In particular, π(y|x) is obtained by collapsing π(y,θ|x) through integrating out θ. This allows the exact computation of π(θ|x) as a mixture distribution without recourse to approximating methods such as MCMC. Useful byproducts of the exact posterior distribution are the marginal likelihood of the model and the exact predictive distribution.

Bibliographic note

© The Author(s) 2013. This article is published with open access at Springerlink.com