## Bayesian Model Averaging And Model Selection For Markov Equivalence Classes Of Acyclic Digraphs (1996)

Venue: | Communications in Statistics: Theory and Methods |

Citations: | 38 - 5 self |

### BibTeX

@INPROCEEDINGS{Madigan96bayesianmodel,

author = {David Madigan and Steen Andersson and Michael Perlman and Chris Volinsky},

title = {Bayesian Model Averaging And Model Selection For Markov Equivalence Classes Of Acyclic Digraphs},

booktitle = {Communications in Statistics: Theory and Methods},

year = {1996},

pages = {2493--2519}

}

### Years of Citing Articles

### OpenURL

### Abstract

Acyclic digraphs (ADGs) are widely used to describe dependences among variables in multivariate distributions. In particular, the likelihood functions of ADG models admit convenient recursive factorizations that often allow explicit maximum likelihood estimates and that are well suited to building Bayesian networks for expert systems. There may, however, be many ADGs that determine the same dependence (= Markov) model. Thus, the family of all ADGs with a given set of vertices is naturally partitioned into Markov-equivalence classes, each class being associated with a unique statistical model. Statistical procedures, such as model selection or model averaging, that fail to take into account these equivalence classes, may incur substantial computational or other inefficiencies. Recent results have shown that each Markov-equivalence class is uniquely determined by a single chain graph, the essential graph, that is itself Markov-equivalent simultaneously to all ADGs in the equivalence clas...

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Citation Context ...turn from Pr(M|T,d) and Pr(T|M,d) defines the required Markov chain for Pr(M,T|d) and thence Pr(M|d) (Besag and Green (1993)). We use Markov chain methods to draw from both conditional distributions (=-=Tierney, 1995-=-, Smith and Roberts, 1993); we devise Hastings-Metropolis algorithms for each one. A total ordering T is said to be compatible with an essential graph M, if v isT v whenever (v i , v j ) is a directed... |

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Citation Context ...en under mild regularity conditions, for any function g(M) defined on , the average: 7 1 1 N g M t t N ( ( )) = is a simulation-consistent estimate of the expectation of g(M) with respect to Pr(M|d) (=-=Smith and Roberts, 1993-=-). To estimate the posterior distribution of some quantity of interest, D, in this manner, set g(M)=Pr(D|M,d). Madigan and York (1995) provide details about parametrizations, prior distributions, and ... |

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