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Biometrika Advance Access published online on October 9, 2009
Biometrika, doi:10.1093/biomet/asp049
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© 2009 Biometrika Trust

Article

Bayesian analysis of matrix normal graphical models

Hao Wang and Mike West

Department of Statistical Science, Duke University, Durham, North Carolina 27708, U.S.A. hao{at}stat.duke.edu mike{at}stat.duke.edu

Received for publication 1 February 2008. Revision received 1 February 2009.
  Abstract

We present Bayesian analyses of matrix-variate normal data with conditional independencies induced by graphical model structuring of the characterizing covariance matrix parameters. This framework of matrix normal graphical models includes prior specifications, posterior computation using Markov chain Monte Carlo methods, evaluation of graphical model uncertainty and model structure search. Extensions to matrix-variate time series embed matrix normal graphs in dynamic models. Examples highlight questions of graphical model uncertainty, search and comparison in matrix data contexts. These models may be applied in a number of areas of multivariate analysis, time series and also spatial modelling.

Key Words: Gaussian graphical model • Graphical model search • Hyper-inverse Wishart distribution • Marginal likelihood • Matrix normal model • Matrix-variate dynamic graphical model • Parameter expansion


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