scholarly journals Markov properties for mixed graphs

Bernoulli ◽  
2014 ◽  
Vol 20 (2) ◽  
pp. 676-696 ◽  
Author(s):  
Kayvan Sadeghi ◽  
Steffen Lauritzen
Keyword(s):  
Mixed Graphs ◽  
Markov Properties

scholarly journals Markov properties of cluster processes

1996 ◽  
Vol 28 (2) ◽  
pp. 346-355 ◽  
Author(s):  
A. J. Baddeley ◽  
M. N. M. Van Lieshout ◽  
J. Møller
Keyword(s):  
Poisson Process ◽  
Point Process ◽  
Markov Property ◽  
Nearest Neighbour ◽  
Finite Range ◽  
Cluster Process ◽  
Cluster Point Process ◽  
Poisson Cluster ◽  
Markov Properties ◽  
Uniformly Bounded

We show that a Poisson cluster point process is a nearest-neighbour Markov point process [2] if the clusters have uniformly bounded diameter. It is typically not a finite-range Markov point process in the sense of Ripley and Kelly [12]. Furthermore, when the parent Poisson process is replaced by a Markov or nearest-neighbour Markov point process, the resulting cluster process is also nearest-neighbour Markov, provided all clusters are non-empty. In particular, the nearest-neighbour Markov property is preserved when points of the process are independently randomly translated, but not when they are randomly thinned.

scholarly journals A Note on Equivalence Classes of Directed Acyclic Independence Graphs

1993 ◽  
Vol 7 (3) ◽  
pp. 409-412 ◽  
Author(s):  
David Madigan
Keyword(s):  
Model Selection ◽  
Expert Systems ◽  
Equivalence Classes ◽  
Influence Diagrams ◽  
Single Class ◽  
Selection Procedures ◽  
Probabilistic Expert Systems ◽  
Recent Developments ◽  
Independence Graphs ◽  
Markov Properties

Directed acyclic independence graphs (DAIGs) play an important role in recent developments in probabilistic expert systems and influence diagrams (Chyu [1]). The purpose of this note is to show that DAIGs can usefully be grouped into equivalence classes where the members of a single class share identical Markov properties. These equivalence classes can be identified via a simple graphical criterion. This result is particularly relevant to model selection procedures for DAIGs (see, e.g., Cooper and Herskovits [2] and Madigan and Raftery [4]) because it reduces the problem of searching among possible orientations of a given graph to that of searching among the equivalence classes.

Singularity of Hermitian (quasi-)Laplacian matrix of mixed graphs

2017 ◽  
Vol 293 ◽  
pp. 287-292 ◽  
Author(s):  
Guihai Yu ◽  
Xin Liu ◽  
Hui Qu
Keyword(s):  
Laplacian Matrix ◽  
Mixed Graphs

scholarly journals On Weak Chromatic Polynomials of Mixed Graphs

2013 ◽  
Vol 31 (1) ◽  
pp. 91-98 ◽  
Author(s):  
Matthias Beck ◽  
Daniel Blado ◽  
Joseph Crawford ◽  
Taïna Jean-Louis ◽  
Michael Young
Keyword(s):  
Chromatic Polynomials ◽  
Mixed Graphs

Markov properties of multiparameter processes and capacities

1995 ◽  
Vol 103 (1) ◽  
pp. 45-71 ◽  
Author(s):  
F. Hirsch ◽  
S. Song
Keyword(s):  
Markov Properties
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