Canonical representation of conditionally specified multivariate discrete distributions
Canonical representation of conditionally specified multivariate discrete distributions
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DOI：
10.1016/j.jmva.2008.11.010
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发表时间：
2009-07-01
影响因子：
1.6
通讯作者：
Wang, Yuchung J.
中科院分区：
文献类型：
--
作者：
Ip, Edward H.;Wang, Yuchung J.
大多数关于条件指定分布的工作都集中在概率空间上的方法上，而概率空间上的约束往往使研究它们的性质具有挑战性。我们建议分解的联合和条件离散分布的特征集的典型的相互作用，我们证明了某些联合分布的相互作用是共享的条件分布。这种不变性为检查涉及同一组变量的条件分布之间的兼容性打开了大门。我们制定的必要和充分条件的离散条件模型的存在性和唯一性，我们展示了如何联合分布可以很容易地计算从池收集的相互作用形式的条件分布。因此，这些方法可以用来计算吉布斯采样器的精确分布。此外，还讨论了如何协调近兼容性等问题。使用混合参数化，我们表明，所提出的方法是基于典型的参数，而传统的方法是基于平均参数。我们的优势部分是由于不变性，仅适用于规范参数。(C)2008年爱思唯尔公司All rights reserved.
Most work on conditionally specified distributions has focused on approaches that operate on the probability space, and the constriants on the probability space often make the study of their properties challenging. We propose decomposing both the joint and conditional discrete distributions in to characterizing sets of canonical interactions, and we prove that certain interactions of a joint distribution are shared with its conditional distributions. This invariance opens the door for checking the compatibility between conditional distributions involving the same set of variables. We formulate necessary and sufficient conditions for the existence and uniqueness of discrete conditional models, and we show how a joint distribution can be easily computed from the pool of interactions collected form the conditional distributions. Hence, the methods can be used to calculate the exact distributions of a Gibbs sampler. Furthermore, issues such as how near compability can be reconciled are also discussed. Using mixed parameterization, we show that the proposed approach is based on the canonical parameters, while the conventional approaches are based on the mean parameters. Our advantage is partly due to the invariance that holds only for the canonical parameters. (C) 2008 Elsevier Inc. All rights reserved.