Independence properties of directed markov fields
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Independence properties of directed markov fields. / Lauritzen, Steffen L.; DAWID, AP; LARSEN, BN; LEIMER, HG.
In: Networks, Vol. 20, No. 5, 1990, p. 491-505.Research output: Contribution to journal › Journal article › Research › peer-review
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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
VL - 20
SP - 491
EP - 505
JO - Networks
JF - Networks
SN - 0028-3045
IS - 5
ER -
ID: 127875713