Zwiernik, Piotr and Smith, J. Q., 1953- (2010) The geometry of independence tree models with hidden variables. Working Paper. University of Warwick. Centre for Research in Statistical Methodology, Coventry.

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Abstract

In this paper we investigate the geometry of undirected discrete graphical models of trees when all the variables in the system are binary, where leaves represent the observable variables and where the inner nodes are unobserved. We obtain a full geometric description of these models which is given by polynomial equations and inequalities. We also give exact formulas for their parameters in terms of the marginal probability over the observed variables. Our analysis is based on combinatorial results generalizing the notion of cumulants and introduce a novel use of Mobius functions on partially ordered sets. The geometric structure we obtain links to the notion of a tree metric considered in phylogenetic analysis and to some interesting determinantal formulas involving hyperdeterminants of 2 x 2 x 2 tables as defined in [19].

Item Type:	Working or Discussion Paper (Working Paper)
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Trees (Graph theory), Multivariate analysis -- Graphic methods
Series Name:	Working papers
Publisher:	University of Warwick. Centre for Research in Statistical Methodology
Place of Publication:	Coventry
Date:	2010
Volume:	Vol.2010
Number:	No.3
Number of Pages:	26
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access
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URI:	http://wrap.warwick.ac.uk/id/eprint/35067

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