Bayesian Estimation for Spherically Symmetric Distributions

The theory of Bayesian least squares is developed for a general and more tangible notion of conjugacy than in models which make the more conventional assumption of normality. This paper is primarily concerned with extending the results of classical conjugate normal-normal Bayesian analysis to the ca...

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Bibliographic Details
Published in:Journal of multivariate analysis 1999-07, Vol.70 (1), p.95-117
Main Authors: Cellier, Dominique, Fourdrinier, Dominique, Wells, Martin T.
Format: Article
Language:English
Subjects:
Bayesian estimation
Bayesian estimation distributions on spheres linear models shrinkage estimate spherical symmetry
Distribution theory
distributions on spheres
Exact sciences and technology
Linear inference, regression
linear models
Mathematics
Multivariate analysis
Probability and statistics
Sciences and techniques of general use
shrinkage estimate
spherical symmetry
Statistics
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Summary:The theory of Bayesian least squares is developed for a general and more tangible notion of conjugacy than in models which make the more conventional assumption of normality. This paper is primarily concerned with extending the results of classical conjugate normal-normal Bayesian analysis to the canonical setting of the generalized linear model when, at the same time, the sampling distribution and the prior are spherically symmetric. In order to underline the intrinsic aspect of our results, the approach of multivariate analysis adopted here is coordinate free. Examples which illustrate the theory are also presented.
ISSN:0047-259X
1095-7243
DOI:10.1006/jmva.1999.1815