Bayesian Models for Directed Graphs
有向图的贝叶斯模型AI 解读 ↓
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分类依据与纠错
AI 根据所提供的论文材料归类：摘要直接研究有向网络的邻接矩阵、节点关系形成能力及关系互惠。
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有向图的贝叶斯模型
- 研究问题
- 有向网络中，如何估计节点吸引和产生关系的能力及互惠倾向，并改善邻接矩阵边际计数较小时的估计问题？
- 方法与思路
- 作者为有向图模型的节点参数设置可交换正态先验，通过边际似然估计协方差分量，并提出近似后验估计程序。
- 材料陈述的贡献
- 摘要称该贝叶斯模型显式考虑节点吸引力与关系扩展能力的关联，且经验例子中的结果可与固定效应模型明显不同。
- 阅读关注点
- 应核对节点参数先验及协方差结构、边际似然算法和后验近似，并查看稀疏边际下结果对先验设定的敏感性。
- 阅读边界
- 仅据 OpenAlex 索引摘要，稿件版本未注明，不能推断刊本变化；结果不同不等于更准确，近似误差也未量化。
原文摘要
Holland and Leinhardt (1981) proposed a simple exponential model called the p 1 model for analyzing digraphs that arise in studies of networks. A digraph consists of a set of g nodes and a g × g adjacency matrix (Xij ), where Xij = 1 if node i relates to node j and Xij = 0 otherwise. The underlying cell probabilities pij = Pr(Xij = 1) are to be estimated from these dichotomous responses. The p 1 model imposes an additive structure on a log-odds version of the pij . It provides information about the abilities of an individual node to attract and to produce relational ties, as well as the tendency of a pair of nodes to reciprocate ties. For digraphs of realistic sizes, the maximum likelihood estimates (MLE's) of the p 1 exponential parameters are often unsatisfactory, particularly when some of the row and column marginal totals of the adjacency matrix are small. A Bayesian approach, using an exchangeable normal prior on the parameters representing the attractiveness and expansiveness characteristics of the nodes, is proposed. The Bayesian p 1 model explicitly recognizes the association between these two characteristics of a node, an important feature ignored by its fixed effects counterpart. An algorithm for finding the MLE's of the covariance components based on a marginal likelihood is presented. An approximate posterior estimation procedure for the exponential parameters is proposed. Using an empirical example, it is shown that the Bayesian p 1 model can yield answers quite different from those of the fixed effects model.