The matrix-F prior for estimating and testing covariance matrices

Joris Mulder, Luis R. Pericchi

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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.
Original languageEnglish
Pages (from-to)1193-1214
JournalBayesian Analysis
Volume13
Issue number4
DOIs
Publication statusPublished - 2018

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F distribution
Covariance matrix
Testing
Intrinsic Priors
Wishart Distribution
Normal distribution
Horseshoe
Generalized Linear Mixed Model
Multivariate Normal Distribution
t-distribution
Gibbs Sampler
Random Effects
Standard deviation
Univariate
Alternatives
Modeling
Simulation

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Mulder, Joris ; Pericchi, Luis R. / The matrix-F prior for estimating and testing covariance matrices. In: Bayesian Analysis. 2018 ; Vol. 13, No. 4. pp. 1193-1214.
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The matrix-F prior for estimating and testing covariance matrices. / Mulder, Joris; Pericchi, Luis R.

In: Bayesian Analysis, Vol. 13, No. 4, 2018, p. 1193-1214.

Research output: Contribution to journalArticleScientificpeer-review

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