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August 2000 Geometry, moments and conditional independence trees with hidden variables
Raffaella Settimi, Jim Q. Smith
Ann. Statist. 28(4): 1179-1205 (August 2000). DOI: 10.1214/aos/1015956712


We study the geometry of the parameter space for Bayesian directed graphical models with hidden variables that have a tree structure and where all the nodes are binary.We show that the conditional independence statements implicit in such models can be expressed in terms of polynomial relationships among the central moments.This algebraic structure will enable us to identify the inequality constraints on the space of the manifest variables that are induced by the conditional independence assumptions as well as determine the degree of unidentifiability of the parameters associated with the hidden variables. By understanding the geometry of the sample space under this class of models we shall propose and discuss simple diagnostic methods.


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Raffaella Settimi. Jim Q. Smith. "Geometry, moments and conditional independence trees with hidden variables." Ann. Statist. 28 (4) 1179 - 1205, August 2000.


Published: August 2000
First available in Project Euclid: 12 March 2002

zbMATH: 1105.62321
MathSciNet: MR1811324
Digital Object Identifier: 10.1214/aos/1015956712

Primary: 62F15
Secondary: 62H17 , 68R10

Keywords: Bayesian multinomial models , Bayesian networks , Conditional independence , model identifiability

Rights: Copyright © 2000 Institute of Mathematical Statistics


Vol.28 • No. 4 • August 2000
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