The matrix-F prior for estimating and testing covariance matrices

Joris Mulder, Luis R. Pericchi

Research output: Contribution to journalArticleScientificpeer-review

22 Citations (Scopus)
211 Downloads (Pure)


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
Issue number4
Publication statusPublished - 2018


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