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May, 1980 Markov Fields and Log-Linear Interaction Models for Contingency Tables
J. N. Darroch, S. L. Lauritzen, T. P. Speed
Ann. Statist. 8(3): 522-539 (May, 1980). DOI: 10.1214/aos/1176345006


We use a close connection between the theory of Markov fields and that of log-linear interaction models for contingency tables to define and investigate a new class of models for such tables, graphical models. These models are hierarchical models that can be represented by a simple, undirected graph on as many vertices as the dimension of the corresponding table. Further all these models can be given an interpretation in terms of conditional independence and the interpretation can be read directly off the graph in the form of a Markov property. The class of graphical models contains that of decomposable models and we give a simple criterion for decomposability of a given graphical model. To some extent we discuss estimation problems and give suggestions for further work.


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J. N. Darroch. S. L. Lauritzen. T. P. Speed. "Markov Fields and Log-Linear Interaction Models for Contingency Tables." Ann. Statist. 8 (3) 522 - 539, May, 1980.


Published: May, 1980
First available in Project Euclid: 12 April 2007

zbMATH: 0444.62064
MathSciNet: MR568718
Digital Object Identifier: 10.1214/aos/1176345006

Primary: 62F99
Secondary: 60K35

Rights: Copyright © 1980 Institute of Mathematical Statistics


Vol.8 • No. 3 • May, 1980
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