Chain Graphs and Symmetric Associations

Graphical models based on chain graphs, which admit both directed and undirected edges, were introduced by by Lauritzen, Wermuth and Frydenberg as a generalization of graphical models based on undirected graphs, and acyclic directed graphs. More recently Andersson, Madigan and Perlman have given an alternative Markov property for chain graphs. This raises two questions: How are the two types of chain graphs to be mterpreted? In which situations should chain graph models be used and with which Markov property?

[1]  Rina Dechter,et al.  Identifying Independencies in Causal Graphs with Feedback , 1996, UAI.

[2]  David Madigan,et al.  An Alternative Markov Property for Chain Graphs , 1996, UAI.

[3]  Nanny Wermuth,et al.  Multivariate Dependencies: Models, Analysis and Interpretation , 1996 .

[4]  M. Frydenberg The chain graph Markov property , 1990 .

[5]  J. Koster,et al.  Markov properties of nonrecursive causal models , 1996 .

[6]  T. Speed,et al.  Markov Fields and Log-Linear Interaction Models for Contingency Tables , 1980 .

[7]  Christopher Meek,et al.  Strong completeness and faithfulness in Bayesian networks , 1995, UAI.

[8]  Thomas S. Richardson,et al.  Causal Inference in the Presence of Latent Variables and Selection Bias , 1995, UAI.

[9]  Thomas S. Richardson,et al.  A Polynomial-Time Algorithm for Deciding Markov Equivalence of Directed Cyclic Graphical Models , 1996, UAI 1996.

[10]  Stephen E. Fienberg,et al.  Discussion of Causal Diagrams for Empirical Research by J. Pearl , 1995 .

[11]  D. Geiger Graphoids: a qualitative framework for probabilistic inference , 1990 .

[12]  M. Studený,et al.  On chain graph models for description of conditional independence structures , 1998 .

[13]  D. A. Kenny,et al.  Correlation and Causation , 1937, Wilmott.

[14]  Judea Pearl,et al.  A Theory of Inferred Causation , 1991, KR.

[15]  P. Spirtes,et al.  Causation, prediction, and search , 1993 .

[16]  Peter Spirtes,et al.  Equivalence of causal models with latent variables , 1992 .

[17]  Mario Stefanelli,et al.  Contribution to the discussion of the paper by Steffen L. Lauritzen and David Spiegelhalter: "Local Computations with Probabilities on Graphical Structures and their Application to Expert Systems" , 1988 .

[18]  J. M. Hammersley,et al.  Markov fields on finite graphs and lattices , 1971 .

[19]  Judea Pearl,et al.  Equivalence and Synthesis of Causal Models , 1990, UAI.

[20]  David Maxwell Chickering,et al.  Learning Bayesian networks: The combination of knowledge and statistical data , 1995, Mach. Learn..

[21]  J. Besag Spatial Interaction and the Statistical Analysis of Lattice Systems , 1974 .

[22]  J. Besag On Spatial-Temporal Models and Markov Fields , 1977 .

[23]  Steffen L. Lauritzen,et al.  Independence properties of directed markov fields , 1990, Networks.

[24]  Peter Spirtes,et al.  Directed Cyclic Graphical Representations of Feedback Models , 1995, UAI.

[25]  F. Fisher A Correspondence Principle for Simultaneous Equation Models , 1970 .

[26]  N. Wermuth,et al.  Graphical Models for Associations between Variables, some of which are Qualitative and some Quantitative , 1989 .

[27]  Thomas S. Richardson,et al.  A Discovery Algorithm for Directed Cyclic Graphs , 1996, UAI.

[28]  J. Pearl Causal diagrams for empirical research , 1995 .