## ANCESTRAL GRAPH MARKOV MODELS (2002)

Citations: | 74 - 17 self |

### BibTeX

@MISC{Richardson02ancestralgraph,

author = {Thomas Richardson and Peter Spirtes},

title = {ANCESTRAL GRAPH MARKOV MODELS },

year = {2002}

}

### Years of Citing Articles

### OpenURL

### Abstract

This paper introduces a class of graphical independence models that is closed under marginalization and conditioning but that contains all DAG independence models. This class of graphs, called maximal ancestral graphs, has two attractive features: there is at most one edge between each pair of vertices; every missing edge corresponds to an independence relation. These features lead to a simple parameterization of the corresponding set of distributions in the Gaussian case.

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Citation Context ...f is by induction on d = jV n un G j. If jdj = 2 then( 1 ) s=(ssj j 1 = 0 as there is no edge $sin G. For jdj > 2, note that by partitioned inversion: ( 1 ) s= ! sfgc 1 cc cfg j f;g:c j 1 (4) = ! sXs;2c ! s1 cc !s! j f;g:c j 1 (5) 58 where c = d n f;sg, and 1 cc =( cc ) 1 . Since andsare not adjacent in (G $ ) a , there is no edge $sin G, hence ! s= 0. Now consider each term i... |

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1 |
for a complete ancestral graph is saturated
- unknown authors
(Show Context)
Citation Context ...n via Recursive Equations with Correlated Errors The Gaussian model N (G) can alternatively be parametrized in two pieces via the factorization of the density: f(x V ) = f(x unG )f(x V nunG j x unG ) =-=(8)-=- The undirected component f unG may be parametrized via an undirected graphical Gaussian model also known as a covariance selection model (see Lauritzen, 1996, Dempster, 1972). The directed component,... |

1 |
when G is not maximal
- unknown authors
(Show Context)
Citation Context ...n via Recursive Equations with Correlated Errors The Gaussian model N (G) can alternatively be parametrized in two pieces via the factorization of the density: f(x V ) = f(x unG )f(x V nunG j x unG ) =-=(8)-=- The undirected component f unG may be parametrized via an undirected graphical Gaussian model also known as a covariance selection model (see Lauritzen, 1996, Dempster, 1972). The directed component,... |

1 |
obeys the global Markov property for G
- unknown authors
(Show Context)
Citation Context ...n via Recursive Equations with Correlated Errors The Gaussian model N (G) can alternatively be parametrized in two pieces via the factorization of the density: f(x V ) = f(x unG )f(x V nunG j x unG ) =-=(8)-=- The undirected component f unG may be parametrized via an undirected graphical Gaussian model also known as a covariance selection model (see Lauritzen, 1996, Dempster, 1972). The directed component,... |

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