Bayesian inference in spherical linear models: robustness and conjugate analysis
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Date
2006
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Publisher
ELSEVIER INC
Abstract
The early work of Zellner on the multivariate Student-t linear model has been extended to Bayesian inference for linear models with dependent non-normal error terms, particularly through various papers by Osiewalski, Steel and coworkers. This article provides a full Bayesian analysis for a spherical linear model. The density generator of the spherical distribution is here allowed to depend both on the precision parameter phi and on the regression coefficients beta. Another distinctive aspect of this paper is that proper priors for the precision parameter are discussed.
The normal-chi-squared family of prior distributions is extended to a new class, which allows the posterior analysis to be carried out analytically. On the other hand, a direct joint modelling of the data vector and of the parameters leads to conjugate distributions for the regression and the precision parameters, both individually and jointly. It is shown that some model specifications lead to Bayes estimators that do not depend on the choice of the density generator, in agreement with previous results obtained in the literature under different assumptions. Finally, the distribution theory developed to tackle the main problem is useful on its own right. (c) 2005 Elsevier Inc. All rights reserved.
The normal-chi-squared family of prior distributions is extended to a new class, which allows the posterior analysis to be carried out analytically. On the other hand, a direct joint modelling of the data vector and of the parameters leads to conjugate distributions for the regression and the precision parameters, both individually and jointly. It is shown that some model specifications lead to Bayes estimators that do not depend on the choice of the density generator, in agreement with previous results obtained in the literature under different assumptions. Finally, the distribution theory developed to tackle the main problem is useful on its own right. (c) 2005 Elsevier Inc. All rights reserved.
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Keywords
linear regression models, elliptical and squared-radial distributions, elliptical density generator, dispersion and dispersion-location elliptical models, Bayes estimator, conjugate families, ELLIPTIC REGRESSION-MODELS