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, Volume 21, Issue 2, pp 274–279 | Cite as

Rejoinder on: Sequences of regressions and their independences

  • Nanny WermuthEmail author
  • Kayvan Sadeghi
Discussion
  • 68 Downloads

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,...

Keywords

Directed Acyclic Graph Undirected Graph Discussion Paper Markov Property Distributional Result 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Sadeghi K (2012) Markov equivalences for subclasses of loopless mixed graphs (submitted). http://arxiv.org/abs/1110.4539
  2. Sadeghi K, Lauritzen SL (2012) Markov properties of mixed graphs. Ann Stat (submitted). http://arxiv.org/abs/1109.5909
  3. Sadeghi K, Marchetti GM (2011). Subroutines available in the R-package ggm vignette Google Scholar
  4. Sadeghi K, Marchetti GM (2012) Graphical Markov models with mixed graphs in R (submitted) Google Scholar
  5. Studený M (2005) Probabilistic conditional independence structures. Springer, London zbMATHGoogle Scholar
  6. Wermuth N (2012) Sequences of regressions and their dependences (submitted). http://arxiv.org/abs/1110.1986
  7. Wermuth N, Cox DR (2004) Joint response graphs and separation induced by triangular systems. J R Stat Soc B 66:687–717 MathSciNetzbMATHCrossRefGoogle Scholar
  8. Wermuth N, Marchetti GM, Cox DR (2009) Triangular systems for symmetric binary variables. Electron J Stat 3:932–955 MathSciNetCrossRefGoogle Scholar
  9. Wermuth N, Marchetti GM, Byrnes G (2012) Case-control studies for rare diseases: improved estimation of several risks and of feature dependences (submitted). http://arxiv.org/abs/1203.1829

Copyright information

© Sociedad de Estadística e Investigación Operativa 2012

Authors and Affiliations

  1. 1.Chalmers Technical UniversityGotherburgSweden
  2. 2.Department of StatisticsUniversity of OxfordOxfordUK

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