Independence properties of directed markov fields
- 1 August 1990
- Vol. 20 (5) , 491-505
- https://doi.org/10.1002/net.3230200503
Abstract
We investigate directed Markov fields over finite graphs without positivity assumptions on the densities involved. A criterion for conditional independence of two groups of variables given a third is given and named as the directed, global Markov property. We give a simple proof of the fact that the directed, local Markov property and directed, global Markov property are equivalent and – in the case of absolute continuity w. r. t. a product measure – equivalent to the recursive factorization of densities. It is argued that our criterion is easy to use, it is sharper than that given by Kiiveri, Speed, and Carlin and equivalent to that of Pearl. It follows that our criterion cannot be sharpened.Keywords
This publication has 10 references indexed in Scilit:
- Influence Diagrams for Statistical ModellingThe Annals of Statistics, 1989
- Graphical Models for Associations between Variables, some of which are Qualitative and some QuantitativeThe Annals of Statistics, 1989
- Local Computations with Probabilities on Graphical Structures and Their Application to Expert SystemsJournal of the Royal Statistical Society Series B: Statistical Methodology, 1988
- A Constraint – Propagation Approach to Probabilistic Reasoning* *This work was supported in part by the National Science Foundation, Grant #DSR 83–13875Published by Elsevier ,1986
- Recursive causal modelsJournal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 1984
- Graphical and Recursive Models for Contingency TablesBiometrika, 1983
- Linear Recursive Equations, Covariance Selection, and Path AnalysisJournal of the American Statistical Association, 1980
- Conditional Independence for Statistical OperationsThe Annals of Statistics, 1980
- Conditional Independence in Statistical TheoryJournal of the Royal Statistical Society Series B: Statistical Methodology, 1979
- The Method of Path CoefficientsThe Annals of Mathematical Statistics, 1934