Geometry, moments and conditional independence trees with hidden variables
成果类型：
Article
署名作者：
Settimi, R; Smith, JQ
署名单位：
University of Chicago; University of Warwick
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
发表日期：
2000
页码：
1179-1205
关键词：
摘要：
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.