an:00005225
Zbl 0743.05065
Lauritzen, S. L.; Dawid, A. P.; Larsen, B. N.; Leimer, H.-G.
Independence properties of directed Markov fields
EN
Networks 20, No. 5, 491-505 (1990).
00155621
1990
j
05C99
directed, local Markov property; directed, global Markov property
Summary: 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.