Probability density decomposition for conditionally dependent random variables modeled by vines
Probability density decomposition for conditionally dependent random variables modeled by vines
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DOI：
10.1023/a:1016725902970
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发表时间：
2001-01-01
影响因子：
1.2
通讯作者：
Cooke, RM
中科院分区：
文献类型：
--
作者：
Bedford, T;Cooke, RM
葡萄树是一种新的相依随机变量图模型。葡萄树推广了常用于多变量分布建模的马尔可夫树。它们与马尔可夫树和贝叶斯信念网的不同之处在于，条件独立的概念被弱化，以允许各种形式的条件依赖。本文导出了依赖于葡萄树的分布的密度的一般公式。这推广了基于将信念网分解为集团的信念网的众所周知的密度公式。此外，该公式允许一个简单的证明信息分解定理的正规葡萄。讨论了条件抽样问题，提出了Gibbs抽样对条件相依分布进行抽样。建立在最高度树上的所谓“典型葡萄树”为吉布斯采样提供了最有效的结构。
A vine is a new graphical model for dependent random variables. Vines generalize the Markov trees often used in modeling multivariate distributions. They differ from Markov trees and Bayesian belief nets in that the concept of conditional independence is weakened to allow for various forms of conditional dependence. A general formula for the density of a vine dependent distribution is derived. This generalizes the well-known density formula for belief nets based on the decomposition of belief nets into cliques. Furthermore, the formula allows a simple proof of the Information Decomposition Theorem for a regular vine. The problem of (conditional) sampling is discussed, and Gibbs sampling is proposed to carry out sampling from conditional vine dependent distributions. The so-called 'canonical vines' built on highest degree trees offer the most efficient structure for Gibbs sampling.