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Bayesian Inference of a Multivariate Regression Model
Joint Authors
Sinay, Marick S.
Hsu, John S. J.
Source
Journal of Probability and Statistics
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-11-23
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Sinay, Marick S.& Hsu, John S. J.. 2014. Bayesian Inference of a Multivariate Regression Model. Journal of Probability and Statistics،Vol. 2014, no. 2014, pp.1-13.
https://search.emarefa.net/detail/BIM-1042828
Modern Language Association (MLA)
Sinay, Marick S.& Hsu, John S. J.. Bayesian Inference of a Multivariate Regression Model. Journal of Probability and Statistics No. 2014 (2014), pp.1-13.
https://search.emarefa.net/detail/BIM-1042828
American Medical Association (AMA)
Sinay, Marick S.& Hsu, John S. J.. Bayesian Inference of a Multivariate Regression Model. Journal of Probability and Statistics. 2014. Vol. 2014, no. 2014, pp.1-13.
https://search.emarefa.net/detail/BIM-1042828
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1042828