A structural Markov property for decomposable graph laws that allows control of clique intersections

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Journal Article
Biometrika, 2018, 105 (1), pp. 19 - 29
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© 2017 Biometrika Trust. We present a new kind of structural Markov property for probabilistic laws on decomposable graphs, which allows the explicit control of interactions between cliques and so is capable of encoding some interesting structure. We prove the equivalence of this property to an exponential family assumption, and discuss identifiability, modelling, inferential and computational implications.
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