Abstract: In the presence of unobserved hidden variables and selection bias, Bayesian networks may not correctly represent causal relationships among the observed variables. Using maximal ancestral graph models, this paper characterizes the independencies and causal structure of the observed variables and provides an algorithm for causal inference using observational data.

Key words: hidden variables, selection bias, Bayesian network, causal inference, maximal ancestral graph

摘要： Bayes网络常用于多变量间的因果推断,但当存在未观测的隐变量和选择变量时，这种图模型往往无法正确描述观测变量间的因果关系。作者利用在观测变量上构造的最大祖先图模型刻画观测变量间的独立性关系和因果结构，并提出了具体的实现算法，从而可由观测数据来推断这类不完全观测下的部分因果关系。

关键词: 隐变量, 选择变量, Bayes网络, 因果推断, 最大祖先图