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Implicit inequality constraints in a binary tree model
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Zwiernik, Piotr and Smith, J. Q. (2011) Implicit inequality constraints in a binary tree model. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. Working papers, Vol.2011 (No.11).
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Official URL: http://www2.warwick.ac.uk/fac/sci/statistics/crism...
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) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > 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 | ||||
Official Date: | 2011 | ||||
Dates: |
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Volume: | Vol.2011 | ||||
Number: | No.11 | ||||
Number of Pages: | 34 | ||||
Institution: | University of Warwick | ||||
Status: | Not Peer Reviewed | ||||
Access rights to Published version: | Open Access (Creative Commons) | ||||
Date of first compliant deposit: | 1 August 2016 | ||||
Date of first compliant Open Access: | 1 August 2016 |
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