INDEPENDENCE PROPERTIES OF DIRECTED MARKOV-FIELDS
INDEPENDENCE PROPERTIES OF DIRECTED MARKOV-FIELDS
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DOI：
10.1002/net.3230200503
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发表时间：
1990-08-01
期刊：
影响因子：
2.1
通讯作者：
LEIMER, HG
中科院分区：
文献类型：
--
作者：
LAURITZEN, SL;DAWID, AP;LEIMER, HG
我们研究有限图上的有向马尔可夫场，其中没有关于密度的正性假设。给出了两组变量条件独立的一个判据，并命名为有向全局马尔可夫性质。我们给出了一个简单的证明，这一事实的定向，局部马尔可夫性质和定向，全球马尔可夫性质是等价的，并-在绝对连续的情况下w。R. t.一个产品措施-相当于递归因式分解的密度。我们认为，我们的标准是易于使用的，它是尖锐的比Kiiveri，速度，和卡林和相当于珍珠。由此可见，我们的标准不能再尖锐了。
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.