We develop Bayesian analysis of matrix-variate normal data with conditional independence graphical structuring of the characterising variance matrix parameters. This development provides a framework for fully Bayesian analysis of matrix normal graphical models, including discussion of novel prior specifications, the resulting problems of posterior computation addressed using Markov chain Monte Carlo methods, and graphical model assessment that involves approximate evaluation of marginal likelihood functions under specified graphical models. Modelling and inference for spatial/image data via a novel class of Markov random fields that arise as natural examples of matrix normal graphical models is discussed. This is complemented by the development of a broad class of dynamic models for matrix-variate time series within which stochastic elements defining time series errors and structural changes over time are subject to graphical model structuring. Three examples illustrate these developments and highlight questions of graphical model uncertainty and comparison in matrix data contexts.

Readers may be interested in software for the MCMC computations and model search as reported in this paper. This archive contains Matlab code and routines for this, and an example in the DEMO.m file.