Exact Bayesian inference via data augmentation

Neal, Peter and Kypraios, Theodore (2015) Exact Bayesian inference via data augmentation. Statistics and Computing, 25 (2). pp. 333-347. ISSN 0960-3174

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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.

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Journal Article
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Statistics and Computing
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© The Author(s) 2013. This article is published with open access at Springerlink.com
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18 Jun 2015 05:55
Last Modified:
22 Nov 2022 01:48