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December 2018 The Matrix-F Prior for Estimating and Testing Covariance Matrices
Joris Mulder, Luis Raúl Pericchi
Bayesian Anal. 13(4): 1193-1214 (December 2018). DOI: 10.1214/17-BA1092

Abstract

The matrix-F distribution is presented as prior for covariance matrices as an alternative to the conjugate inverted Wishart distribution. A special case of the univariate F distribution for a variance parameter is equivalent to a half-t distribution for a standard deviation, which is becoming increasingly popular in the Bayesian literature. The matrix-F distribution can be conveniently modeled as a Wishart mixture of Wishart or inverse Wishart distributions, which allows straightforward implementation in a Gibbs sampler. By mixing the covariance matrix of a multivariate normal distribution with a matrix-F distribution, a multivariate horseshoe type prior is obtained which is useful for modeling sparse signals. Furthermore, it is shown that the intrinsic prior for testing covariance matrices in non-hierarchical models has a matrix-F distribution. This intrinsic prior is also useful for testing inequality constrained hypotheses on variances. Finally through simulation it is shown that the matrix-variate F distribution has good frequentist properties as prior for the random effects covariance matrix in generalized linear mixed models.

Citation

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Joris Mulder. Luis Raúl Pericchi. "The Matrix-F Prior for Estimating and Testing Covariance Matrices." Bayesian Anal. 13 (4) 1193 - 1214, December 2018. https://doi.org/10.1214/17-BA1092

Information

Published: December 2018
First available in Project Euclid: 12 January 2018

zbMATH: 06989981
MathSciNet: MR3855368
Digital Object Identifier: 10.1214/17-BA1092

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Vol.13 • No. 4 • December 2018
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