This paper presents the Bayes estimation and empirical Bayes estimation of causal effects in a counterfactual model. It also gives three kinds of prior distribution of the assumptions of replaceability. The experiment shows that empirical Bayes estimation is better than other estimations when not knowing which assumption is true.
A chain graph allows both directed and undirected edges, and contains the underlying mathematical properties of the two. An important method of learning graphical models is to use scoring criteria to measure how well the graph structures fit the data. In this paper, we present a scoring criterion for learning chain graphs based on the Kullback Leibler distance. It is score equivalent, that is, equivalent chain graphs obtain the same score, so it can be used to perform model selection and model averaging.
