Open Access
June 2011 Separable covariance arrays via the Tucker product, with applications to multivariate relational data
Peter D. Hoff
Bayesian Anal. 6(2): 179-196 (June 2011). DOI: 10.1214/11-BA606


Modern datasets are often in the form of matrices or arrays, potentially having correlations along each set of data indices. For example, data involving repeated measurements of several variables over time may exhibit temporal correlation as well as correlation among the variables. A possible model for matrix-valued data is the class of matrix normal distributions, which is parametrized by two covariance matrices, one for each index set of the data. In this article we discuss an extension of the matrix normal model to accommodate multidimensional data arrays, or tensors. We show how a particular array-matrix product can be used to generate the class of array normal distributions having separable covariance structure. We derive some properties of these covariance structures and the corresponding array normal distributions, and show how the array-matrix product can be used to define a semi-conjugate prior distribution and calculate the corresponding posterior distribution. We illustrate the methodology in an analysis of multivariate longitudinal network data which take the form of a four-way array.


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Peter D. Hoff. "Separable covariance arrays via the Tucker product, with applications to multivariate relational data." Bayesian Anal. 6 (2) 179 - 196, June 2011.


Published: June 2011
First available in Project Euclid: 13 June 2012

zbMATH: 1330.62132
MathSciNet: MR2806238
Digital Object Identifier: 10.1214/11-BA606

Primary: 62F15
Secondary: 60E05 , 62H05 , 62H12 , 62J10 , 62P20

Keywords: Gaussian , matrix normal , multiway data , network , tensor , Tucker decomposition

Rights: Copyright © 2011 International Society for Bayesian Analysis

Vol.6 • No. 2 • June 2011
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