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Application of a predictive distribution formula to Bayesian computation for incomplete data models

Sweeting, T. and Kharroubi, S. (2005) Application of a predictive distribution formula to Bayesian computation for incomplete data models. Statistics & Computing, 15 (3). pp. 167-178. ISSN 1573-1375

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Abstract

We consider exact and approximate Bayesian computation in the presence of latent variables or missing data. Specifically we explore the application of a posterior predictive distribution formula derived in Sweeting And Kharroubi (2003), which is a particular form of Laplace approximation, both as an importance function and a proposal distribution. We show that this formula provides a stable importance function for use within poor man’s data augmentation schemes and that it can also be used as a proposal distribution within a Metropolis-Hastings algorithm for models that are not analytically tractable. We illustrate both uses in the case of a censored regression model and a normal hierarchical model, with both normal and Student t distributed random effects. Although the predictive distribution formula is motivated by regular asymptotic theory, it is not necessary that the likelihood has a closed form or that it possesses a local maximum.

Item Type: Article
Academic Units: The University of York > Mathematics (York)
Depositing User: York RAE Import
Date Deposited: 10 Feb 2009 12:37
Last Modified: 10 Feb 2009 12:37
Published Version: http://dx.doi.org/10.1007/s11222-005-1306-9
Status: Published
Publisher: Springer
Identification Number: 10.1007/s11222-005-1306-9
URI: http://eprints.whiterose.ac.uk/id/eprint/7537

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