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.
Publié le : 2000-08-14
Classification:
Conditional independence,
Bayesian networks,
Bayesian multinomial models,
model identifiability,
62F15,
62H17,
68R10
@article{1015956712,
author = {Settimi, Raffaella and Smith, Jim Q.},
title = {Geometry, moments and conditional independence trees with hidden
variables},
journal = {Ann. Statist.},
volume = {28},
number = {3},
year = {2000},
pages = { 1179-1205},
language = {en},
url = {http://dml.mathdoc.fr/item/1015956712}
}
Settimi, Raffaella; Smith, Jim Q. Geometry, moments and conditional independence trees with hidden
variables. Ann. Statist., Tome 28 (2000) no. 3, pp. 1179-1205. http://gdmltest.u-ga.fr/item/1015956712/