A class of smooth models satisfying marginal and context specific conditional independencies

R. Colombi; A. Forcina

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arXiv · 1210.8050

A class of smooth models satisfying marginal and context specific conditional independencies

R. Colombi·A. Forcina

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Abstract

We study a class of conditional independence models for discrete data with the property that one or more log-linear interactions are defined within two different marginal distributions and then constrained to 0; all the conditional independence models which are known to be non smooth belong to this class. We introduce a new marginal log-linear parameterization and show that smoothness may be restored by restricting one or more independence statements to hold conditionally to a restricted subset of the configurations of the conditioning variables. Our results are based on a specific reconstruction algorithm from log-linear parameters to probabilities and fixed point theory. Several examples are examined and a general rule for determining the implied conditional independence restrictions is outlined.

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R. Colombi, A. Forcina. 2012-10-30. A class of smooth models satisfying marginal and context specific conditional independencies. https://arxiv.org/abs/1210.8050

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