CONDITIONALLY EXTERNALLY BAYESIAN POOLING OPERATORS IN CHAIN GRAPHS
CONDITIONALLY EXTERNALLY BAYESIAN POOLING OPERATORS IN CHAIN GRAPHS
复制标题
链图中的条件外部贝叶斯池算子
DOI：
10.1214/aos/1031594740
复制
发表时间：
1997
影响因子：
4.5
通讯作者：
Jim Q. Smith
中科院分区：
文献类型：
--
作者：
Á. E. Faria;Jim Q. Smith
我们讨论了多变量版本的Franch的群决策问题，其中m个群成员共同负责他们应该做出的决策，他们希望将他们对n个随机变量的可能值的信念结合到群共识概率分布中。我们将假设小组已经就问题中变量的关联结构达成一致，正如我们在论文中定义的共同同意的部分完全链图(PCG)所表示的那样。然而，成员们对共同PCG中变量的实际条件概率分布存在分歧。我们建议他们采用的组合算法至少要求成员共同的学习信息并保持最初商定的PCG结构，即与PCG相关的条件分布池是外部贝叶斯(EB)的。我们给出了这类条件EB(CEB)池的一个刻画，它比Genest，McConway和Schervish提出的刻画更具一般性和灵活性。具体地说，这样的概括允许归因于池中不同个体的联合概率评估的权重在每个联合密度的不同分量上不同。我们证明，当群同意以与图中证据传播兼容的顺序执行条件汇集时，群在链元素上成为CEB的承诺可以通过群在整个PCG上是EB来实现。
We address the multivariate version of French's group decision problem where the m members of a group, who are jointly responsible for the decisions they should make, wish to combine their beliefs about the possible values of n random variables into the group consensus probability distribution. We shall assume the group has agreed on the structure of associations of variables in a problem, as might be represented by a commonly agreed partially complete chain graph (PCG) we define in the paper. However, the members diverge about the actual conditional probability distributions for the variables in the common PCG. The combination algorithm we suggest they adopt is one which demands, at least on learning information which is common to the members and which preserves the originally agreed PCG structure, that the pools of conditional distributions associated with the PCG are externally Bayesian (EB). We propose a characterization for such conditionally EB (CEB) poolings which is more general and flexible than the characterization proposed by Genest, McConway and Schervish. In particular, such a generalization allows the weights attributed to the joint probability assessments of different individuals in the pool to differ across the distinct components of each joint density. We show that the group's commitment to being CEB on chain elements can be accomplished by the group being EB on the whole PCG when the group also agrees to perform the conditional poolings in an ordering compatible with evidence propagation in the graph.