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.

Bayesian analysis of matrix-variate normal data with conditional independencies can improve model structure search and uncertainty evaluation in multivariate analysis, time series, and spatial modeling.

Bayesian analysis of matrix normal graphical models.

Key Takeaway: Bayesian analysis of matrix-variate normal data with conditional independencies can improve model structure search and uncertainty evaluation in multivariate analysis, time series, and spatial modeling.