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Implicit inequality constraints in a binary tree model
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Zwiernik, Piotr and Smith, J. Q., 1953 (2011) Implicit inequality constraints in a binary tree model. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. (Working papers).

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Abstract
In this paper we investigate the geometry of a discrete Bayesian network whose graph is a tree all of whose variables are binary and the only observed variables are those labeling its leaves. We provide the full geometric description of these models which is given by a set of polynomial equations together with a set of complementary implied inequalities induced by the positivity of probabilities on hidden variables. The phylogenetic invariants given by the equations can be useful in the construction of simple diagnostic tests. However, in this paper we point out the importance of also incorporating the associated inequalities into any statistical analysis. The full characterization of these inequality constraints derived in this paper helps us determine now why routine statistical methods can break down for this model class.
Item Type:  Working or Discussion Paper (Working Paper) 

Subjects:  Q Science > QA Mathematics 
Divisions:  Faculty of Science > Statistics 
Library of Congress Subject Headings (LCSH):  Bayesian statistical decision theory, Graph theory 
Series Name:  Working papers 
Publisher:  University of Warwick. Centre for Research in Statistical Methodology 
Place of Publication:  Coventry 
Date:  2011 
Volume:  Vol.2011 
Number:  No.11 
Number of Pages:  34 
Status:  Not Peer Reviewed 
Access rights to Published version:  Open Access 
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URI:  http://wrap.warwick.ac.uk/id/eprint/34881 
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