A simple algorithm for checking compatibility among discrete conditional distributions
A simple algorithm for checking compatibility among discrete conditional distributions
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DOI：
10.1016/j.csda.2011.02.017
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发表时间：
2011-08-01
影响因子：
1.8
通讯作者：
Wang, Yuchung J.
中科院分区：
文献类型：
--
作者：
Kuo, Kun-Lin;Wang, Yuchung J.
当只有条件分布已知或可用时，分布被称为条件指定的。第一个问题总是相容性：是否存在一个能够复制所有条件分布的联合分布？我们回顾了自2002年以来发表的五种方法-主要是两个或三个变量，我们得出的结论是，这些方法要么在数学上太复杂，要么太难（在许多情况下是不可能的）推广到高维。本文的目的是提出一种通用算法，可以以简单的方式有效地验证兼容性。我们的方法直观简单，一般足以处理任何全条件规格。此外，我们说明的现象，两个理论上等价的条件模型可以是不同的兼容性，或可以导致不同的联合分布。这种现象的影响也进行了讨论。(C)2011 Elsevier B. V.保留所有权利。
A distribution is said to be conditionally specified when only its conditional distributions are known or available. The very first issue is always compatibility: does there exist a joint distribution capable of reproducing all of the conditional distributions? We review five methods - mostly for two or three variables - published since 2002, and we conclude that these methods are either mathematically too involved and/or are too difficult (and in many cases impossible) to generalize to a high dimension. The purpose of this paper is to propose a general algorithm that can efficiently verify compatibility in a straightforward fashion. Our method is intuitively simple and general enough to deal with any full-conditional specifications. Furthermore, we illustrate the phenomenon that two theoretically equivalent conditional models can be different in terms of compatibilities, or can result in different joint distributions. The implications of this phenomenon are also discussed. (C) 2011 Elsevier B.V. All rights reserved.