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Independence properties of directed markov fields
Author(s) -
Lauritzen S. L.,
Dawid A. P.,
Larsen B. N.,
Leimer H.G.
Publication year - 1990
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.3230200503
Subject(s) - markov chain , mathematics , independence (probability theory) , markov property , simple (philosophy) , markov process , conditional independence , property (philosophy) , markov kernel , factorization , markov model , measure (data warehouse) , variable order markov model , directed graph , discrete mathematics , combinatorics , statistics , computer science , algorithm , philosophy , epistemology , database
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.