Multivariate Bayesian variable selection and prediction

Brown, Philip J. and Vannucci, Marina and Fearn, T. (1998) Multivariate Bayesian variable selection and prediction. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 60 . pp. 627-41. ISSN 1369-7412. (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

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The multivariate regression model is considered with p regressors. A latent vector with p binary entries serves to identify one of two types of regression coefficients: those close to 0 and those not. Specializing our general distributional setting to the linear model with Gaussian errors and using natural conjugate prior distributions, we derive the marginal posterior distribution of the binary latent vector. Fast algorithms aid its direct computation, and in high dimensions these are supplemented by a Markov chain Monte Carlo approach to sampling from the known posterior distribution. Problems with hundreds of regressor variables become quite feasible. We give a simple method of assigning the hyperparameters of the prior distribution. The posterior predictive distribution is derived and the approach illustrated on compositional analysis of data involving three sugars with 160 near infra-red absorbances as regressors.

Item Type: Article
Uncontrolled keywords: Bayesian selection; conjugate distributions; latent variables; Markov chain Monte Carlo method; model averaging; multivariate regression; prediction
Subjects: Q Science > QA Mathematics (inc Computing science) > QA276 Mathematical statistics
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science
Depositing User: I. Ghose
Date Deposited: 05 Apr 2009 10:03
Last Modified: 13 May 2014 11:16
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