Open Access
Translator Disclaimer
December, 1993 Logical and Algorithmic Properties of Conditional Independence and Graphical Models
Dan Geiger, Judea Pearl
Ann. Statist. 21(4): 2001-2021 (December, 1993). DOI: 10.1214/aos/1176349407


This article develops an axiomatic basis for the relationship between conditional independence and graphical models in statistical analysis. In particular, the following relationships are established: (1) every axiom for conditional independence is an axiom for graph separation, (2) every graph represents a consistent set of independence and dependence constraints, (3) all binary factorizations of strictly positive probability models can be encoded and determined in polynomial time using their correspondence to graph separation, (4) binary factorizations of non-strictly positive probability models can also be derived in polynomial time albeit less efficiently and (5) unconditional independence relative to normal models can be axiomatized with a finite set of axioms.


Download Citation

Dan Geiger. Judea Pearl. "Logical and Algorithmic Properties of Conditional Independence and Graphical Models." Ann. Statist. 21 (4) 2001 - 2021, December, 1993.


Published: December, 1993
First available in Project Euclid: 12 April 2007

zbMATH: 0814.62006
MathSciNet: MR1245778
Digital Object Identifier: 10.1214/aos/1176349407

Primary: 60A05
Secondary: 60G60, 60J99, 62A15, 62H25

Rights: Copyright © 1993 Institute of Mathematical Statistics


Vol.21 • No. 4 • December, 1993
Back to Top