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Biometrika 1981 68(1):265-274; doi:10.1093/biomet/68.1.265
© 1981 by Biometrika Trust
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Some matrix-variate distribution theory: Notational considerations and a Bayesian application

A. P. DAWID

Department of Mathematics, The City University London

We introduce and justify a convenient notation for certain matrix-variate distributions which, by its emphasis on the important underlying parameters, and the theory on which it is based, eases greatly the task of manipulating such distributions. Important examples include the matrix-variate normal, t, F and beta, and the Wishart and inverse Wishart distributions. The theory is applied to compound matrix distributions and to Bayesian prediction in the multivariate linear model.

Key Words: Bayesian prediction • Compound distribution • Extendible • Inverse Wishart • Matrix beta • Matrix F • Matrix t • Multivariate linear model • Random matrix • Rotatable • Scale matrix • Spherical • Wishart


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