Alternative Markov properties for chain graphs
Alternative Markov properties for chain graphs
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DOI：
10.1111/1467-9469.00224
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发表时间：
2001-03-01
影响因子：
1
通讯作者：
Perlman, MD
中科院分区：
文献类型：
--
作者：
Andersson, SA;Madigan, D;Perlman, MD
图形马尔可夫模型使用图形来表示统计变量之间可能的依赖性。 Lauritzen、Wermuth 和 Frydenberg (LWF) 引入了链图 (CG) 的马尔可夫性质：可用于同时表示结构依赖性和关联依赖性的图，并且包括作为特殊情况的无向图 (UG) 和非循环有向图 (ADG)。这里引入了 CG 的替代马尔可夫性质 (AMP)，并证明它是具有多元正态误差的块递归线性系统所满足的马尔可夫性质。该模型可以分解为条件正态模型的集合，每个条件正态模型都结合了多元线性回归模型和协方差选择模型的特征，便于对其参数的估计。在一般情况下，给出了 CG 的 LWF 和 AMP 马尔可夫性质等价、两个 CG 的 AMP 马尔可夫等价、CG 与某些 ADG 或可分解 UG 的 AMP 马尔可夫等价以及其他等价的充分必要条件。对于 CG，在某些方面，AMP 属性是 ADG 马尔可夫属性比 LWP 属性更直接的扩展。
Graphical Markov models use graphs to represent possible dependences among statistical variables. Lauritzen, Wermuth, and Frydenberg (LWF) introduced a Markov property for chain graphs (CG): graphs that can be used to represent both structural and associative dependences simultaneously and that include both undirected graphs (UG) and acyclic directed graphs (ADG) as special cases. Here an alternative Markov property (AMP) for CGs is introduced and shown to be the Markov property satisfied by a block-recursive linear system with multivariate normal errors. This model can be decomposed into a collection of conditional normal models, each of which combines the features of multivariate linear regression models and covariance selection models, facilitating the estimation of its parameters. In the general case, necessary and sufficient conditions are given for the equivalence of the LWF and AMP Markov properties of a CG, for the AMP Markov equivalence of two CGs, for the AMP Markov equivalence of a CG to some ADG or decomposable UG, and for other equivalences. For CGs, in some ways the AMP property is a more direct extension of the ADG Markov property than is the LWP property.