Rejoinder on: Sequences of regressions and their independences
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We thank the discussants for their careful reading of the manuscript and their thoughtful comments. It is nice to see that almost each discussant stresses a different contribution of the paper, that the paper initiated already extensions of distributional results and that many other special aspects are emphasized in the discussions. We respond in detail to the comments, with the discussants ordered alphabetically.
Response to Dr. Robert Castelo
We agree with Robert that the global Markov property of concentration graphs, also known as their separation criterion, is simple and computationally more attractive than those for directed acyclic graphs and regression graphs. However, concentration graphs have also only one type of edge so that they do not, for instance, permit to integrate a priori available knowledge about a time ordering among the variables into model building processes.
Furthermore, if such an ordering holds and leads to simplifying factorizations of the joint density,...
KeywordsDirected Acyclic Graph Undirected Graph Discussion Paper Markov Property Distributional Result
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