The matrix-F prior for estimating and testing covariance matrices

 

I am proud that our paper “The matrix-F prior for estimating and testing covariance matrices “, written by me and Luis Raúl Pericchi, got published in Bayesian Analysis. In the paper we propose the matrix-F distribution as an alternative for the inverse Wishart distribution as a prior to model covariance matrices. We highlight various useful properties of this prior in challenging Bayesian modeling problems. In particular it is shown how the prior can be implemented in a Gibbs sampler using a parameter extension. 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. 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. The paper can be freely downloaded here.

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