Independence properties of directed markov fields

TY - JOUR

T1 - Independence properties of directed markov fields

AU - Lauritzen, Steffen L.

AU - DAWID, AP

AU - LARSEN, BN

AU - LEIMER, HG

PY - 1990

Y1 - 1990

N2 - 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.

AB - 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.

U2 - 10.1002/net.3230200503

DO - 10.1002/net.3230200503

M3 - Journal article

SN - 0028-3045

VL - 20

SP - 491

EP - 505

JO - Networks

JF - Networks

IS - 5

ER -