Bayesian Inference of a Multivariate Regression Model

We explore Bayesian inference of a multivariate linear regression model with use of a flexible prior for the covariance structure. The commonly adopted Bayesian setup involves the conjugate prior, multivariate normal distribution for the regression coefficients and inverse Wishart specification for...

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Bibliographic Details
Published in:Journal of probability and statistics 2014-01, Vol.2014 (2014), p.1-13
Main Authors: Sinay, Marick S., Hsu, John S. J.
Format: Article
Language:English
Subjects:
Algorithms
Bayesian analysis
Covariance
Covariance matrix
Density
Economic models
Estimates
Inference
Integral equations
Mathematical models
Regression
Students
Variables
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Summary:We explore Bayesian inference of a multivariate linear regression model with use of a flexible prior for the covariance structure. The commonly adopted Bayesian setup involves the conjugate prior, multivariate normal distribution for the regression coefficients and inverse Wishart specification for the covariance matrix. Here we depart from this approach and propose a novel Bayesian estimator for the covariance. A multivariate normal prior for the unique elements of the matrix logarithm of the covariance matrix is considered. Such structure allows for a richer class of prior distributions for the covariance, with respect to strength of beliefs in prior location hyperparameters, as well as the added ability, to model potential correlation amongst the covariance structure. The posterior moments of all relevant parameters of interest are calculated based upon numerical results via a Markov chain Monte Carlo procedure. The Metropolis-Hastings-within-Gibbs algorithm is invoked to account for the construction of a proposal density that closely matches the shape of the target posterior distribution. As an application of the proposed technique, we investigate a multiple regression based upon the 1980 High School and Beyond Survey.
ISSN:1687-952X
1687-9538
DOI:10.1155/2014/673657