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Posterior mean and variance approximation for regression and time series problems

Triantafyllopoulos, K. and Harrison, P.J. (2008) Posterior mean and variance approximation for regression and time series problems. Statistics, 42 (4). pp. 329-350. ISSN 0233-1888

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This paper develops a methodology for approximating the posterior first two moments of the posterior distribution in Bayesian inference. Partially specified probability models that are defined only by specifying means and variances, are constructed based upon second-order conditional independence in order to facilitate posterior updating and prediction of required distributional quantities. Such models are formulated particularly for multivariate regression and time series analysis with unknown observational variance-covariance components. The similarities and differences of these models with the Bayes linear approach are established. Several subclasses of important models, including regression and time series models with errors following multivariate t, inverted multivariate t and Wishart distributions, are discussed in detail. Two numerical examples consisting of simulated data and of US investment and change in inventory data illustrate the proposed methodology.

Item Type: Article
Copyright, Publisher and Additional Information: © 2008 Taylor & Francis. This is an author produced version of a paper subsequently published in Statistics. Uploaded in accordance with the publisher's self-archiving policy.
Keywords: Bayesian inference; conditional independence; regression; time series; Bayes linear methods; state space models; dynamic linear models; Kalman filter; Bayesian forecasting
Institution: The University of Sheffield
Academic Units: The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield)
Depositing User: Mrs Megan Hobbs
Date Deposited: 29 Mar 2010 12:28
Last Modified: 17 Nov 2015 08:08
Published Version: http://dx.doi.org/10.1080/02331880701864978
Status: Published
Publisher: Taylor & Francis
Identification Number: 10.1080/02331880701864978
Related URLs:
URI: http://eprints.whiterose.ac.uk/id/eprint/10624

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