Separable covariance arrays via the Tucker product, with applications to multivariate relational data

Bayesian Analysis

Volumn 6, Issue 2, 2011, Pages 179-196

  Hoff, Peter D ^a  

^a UNIVERSITY OF WASHINGTON   (United States)

Author keywords

Gaussian; Matrix normal; Multiway data; Network; Tensor; Tucker decomposition

Indexed keywords

EID: 79958754282     PISSN: 19360975     EISSN: 19316690     Source Type: Journal    
DOI: 10.1214/11-BA606     Document Type: Article

References (20)

1. Browne, M. W. and Shapiro, A. (1991). "Invariance of covariance structures under groups of transformations." Metrika, 38(6): 345-355
2. Carvalho, C. M. and West, M. (2007). "Dynamic Matrix-variate Graphical Models." Bayesian Analysis, 2(1): 69-98
3. Dawid, A. P. (1981). "Some matrix-variate distribution theory: notational considerations and a Bayesian application." Biometrika, 68(1): 265-274
4. De Lathauwer, L., De Moor, B., and Vandewalle, J. (2000). "A multilinear singular value decomposition." SIAM Journal on Matrix Analysis and Applications, 21(4): 1253-1278
5. Dutilleul, P. (1999). "The MLE algorithm for the matrix normal distribution." Journal of Statistical Computation and Simulation, 64(2): 105-123
6. Galecki, A. (1994). "General class of covariance structures for two or more repeated fac-tors in longitudinal data analysis." Communications in Statistics-Theory and Methods, 23(11): 3105-3119
7. Kass, R. E. and Wasserman, L. (1995). "A reference Bayesian test for nested hypotheses and its relationship to the Schwarz criterion." J. Amer. Statist. Assoc., 90(431): 928-934
8. Kolda, T. G. (2006). "Multilinear operators for higher-order decompositions." Technical Report SAND2006-2081, Sandia National Laboratories, Albuquerque, NM and Livermore, CA
9. Kroonenberg, P. M. (2008). Applied multiway data analysis. Wiley Series in Probability and Statistics. Hoboken, NJ: Wiley-Interscience [John Wiley & Sons]. With a foreword by Willem J. Heiser and Jarqueline Meulman
10. Lu, N. and Zimmerman, D. L. (2005). "The likelihood ratio test for a separable covariance matrix." Statist. Probab. Lett., 73(4): 449-457
11. McCullagh, P. (1987). Tensor methods in statistics. Monographs on Statistics and Applied Probability. London: Chapman & Hall
12. Mitchell, M. W., Genton, M. G., and Gumpertz, M. L. (2006). "A likelihood ratio test for separability of covariances." J. Multivariate Anal., 97(5): 1025-1043
13. Quintana, J. M. and West, M. (1988). "Time Series Analysis of Compositional Data." In Bernardo, J. M., DeGroot, M. H., Lindley, D. V., and Smith, A. F. M. (eds.), Bayesian Statistics 3, 747-756. Clarendon Press [Oxford University Press]
14. Roy, A. and Khattree, R. (2005). "On implementation of a test for Kronecker product covariance structure for multivariate repeated measures data." Stat. Methodol., 2(4): 297-306
15. Rubin, D. B. (1984). "Bayesianly justifiable and relevant frequency calculations for the applied statistician." Ann. Statist., 12(4): 1151-1172
16. Tseng, P. (2001). "Convergence of a block coordinate descent method for nondifferen-tiable minimization." J. Optim. Theory Appl., 109(3): 475-494
17. Tucker, L. (1966). "Some mathematical notes on three-mode factor analysis." Psychometrika, 31(3): 279-311
18. Tucker, L. R. (1964). "The extension of factor analysis to three-dimensional matrices." Contributions to mathematical psychology, 109-127
19. Wang, H. and West, M. (2009). "Bayesian analysis of matrix normal graphical models." Biometrika, 96(4): 821-834
20. West, M. and Harrison, J. (1997). Bayesian forecasting and dynamic models. Springer Series in Statistics. New York: Springer-Verlag, second edition.