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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. Electronic Journal of Statistics, Vol.5 . pp. 1276-1312. doi:10.1214/11-EJS640 ISSN 1935-7524.
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Official URL: http://dx.doi.org/10.1214/11-EJS640
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 implies inequalities induces 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 how and why routine statistical methods can break down for this model class.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
Library of Congress Subject Headings (LCSH): | Graphical modeling (Statistics), Decision trees, Trees (Graph theory) | ||||
Journal or Publication Title: | Electronic Journal of Statistics | ||||
Publisher: | Institute of Mathematical Statistics | ||||
ISSN: | 1935-7524 | ||||
Official Date: | 2011 | ||||
Dates: |
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Volume: | Vol.5 | ||||
Page Range: | pp. 1276-1312 | ||||
DOI: | 10.1214/11-EJS640 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Open Access (Creative Commons) |
Data sourced from Thomson Reuters' Web of Knowledge
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