MARKOV PROPERTIES FOR LOOPLESS MIXED GRAPHS

[1]  Peter Clifford,et al.  Markov Random Fields in Statistics , 2012 .

[2]  N. Wermuth.  PROBABILITY DISTRIBUTIONS WITH SUMMARY GRAPH STRUCTURE , 2010, 1003.3259.

[3]  Jin Tian,et al.  Markov Properties for Linear Causal Models with Correlated Errors , 2009, J. Mach. Learn. Res..

[4]  M. Drton.  Discrete chain graph models , 2009, 0909.0843.

[5]  N. Wermuth,et al.  Triangular systems for symmetric binary variables , 2009 .

[6]  J. Koster.  Marginalizing and conditioning in graphical models , 2002 .

[7]  P. Spirtes,et al.  Ancestral graph Markov models , 2002 .

[8]  D. Madigan,et al.  Alternative Markov Properties for Chain Graphs , 2001 .

[9]  Nanny Wermuth,et al.  On association models defined over independence graphs , 1998 .

[10]  Christopher Meek,et al.  The dimensionality of mixed ancestral graphs , 1997 .

[11]  N. Wermuth,et al.  Linear Dependencies Represented by Chain Graphs , 1993 .

[12]  Dan Geiger,et al.  Identifying independence in bayesian networks , 1990, Networks.

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

[14]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[15]  T. Speed,et al.  Recursive causal models , 1984, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics.

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

[17]  A. Dawid.  Conditional Independence in Statistical Theory , 1979 .

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

[19]  G. Grimmett.  A THEOREM ABOUT RANDOM FIELDS , 1973 .

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