Probability distributions with summary graph structure. (English) Zbl 1245.62062
Graphs are used to specify the independence structures present among the component random variables in a multivariate probability distribution. By considering implications that can be derived after marginalising over some variables or after conditioning on others, graphs can be obtained that capture these independence structures. Different classes of such independence-preserving graphs are discussed and compared. Properties of so called summary graphs are derived and interpreted as special types of paths in graphs.
Reviewer: Ove Frank (Stockholm)
MSC:
| 62H05 | Characterization and structure theory for multivariate probability distributions; copulas |
| 05C90 | Applications of graph theory |
| 05C20 | Directed graphs (digraphs), tournaments |
Keywords:
independence graph; concentration graph; covariance graph; regression graph; directed acyclic graph; graphical Markov model; dependence confounding; triangular systemSoftware:
TETRADReferences:
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