Vines inference. (English) Zbl 1272.62040

Kurowicka, D.; Cooke, R. M.; Callies, U.

Braz. J. Probab. Stat. 21, No. 1, 103-120 (2007).

Summary: In this paper, vines [R. M. Cooke, “Markov and entropy properties of tree- and vine-dependent variables”, in: Proceedings of the ASA section of Bayesian statistical science (1997); T. Bedford and R. M. Cooke, Ann. Stat. 30, No. 4, 1031–1068 (2002; Zbl 1101.62339)] are reviewed. We prove that the product of 1 minus the square of partial correlations on a vine equals the determinant of the correlation matrix. This is used in learning vines. In model learning we are interested in models incorporating maximal (conditional) independence with minimal disturbance. This leads us to search for regular vines whose associated factorization of the determinant is dominant in the sense of majorization. We compare this with the method of independence graphs [J. Whittaker, Graphical models in applied multivariate statistics. Chichester: John Wiley & Sons Ltd. xiv, 448p. (1990; Zbl 0732.62056)].

MSC:

62H05	Characterization and structure theory for multivariate probability distributions; copulas
62H99	Multivariate analysis
62A09	Graphical methods in statistics
05C05	Trees
05C90	Applications of graph theory

Keywords:

graphical models; independence graphs; inference; vines

Citations:

Zbl 1101.62339; Zbl 0732.62056