Marginal log-linear parameters for graphical Markov models

Details Marginal log-linear parameters for graphical Markov models Marginal log-linear parameters for graphical Markov models

2011-05-30

arxiv.org/abs/1105.6075v1

Statistics

Methodology

26 pages

Scientific paper

The parametrization of multivariate discrete statistical models by marginal log-linear (MLL) parameters provides a great deal of flexibility; in particular, different MLL parametrizations under linear constraints induce various sub-models, including models defined by some collections of conditional independences. Such models are curved exponential families, and therefore have regular asymptotic properties. We introduce a sub-class of MLL models which correspond to Acyclic Directed Mixed Graphs under the usual global Markov property. We characterize for precisely which graphs the resulting parametrization is variation independent, and show how it is both intuitive, and easily adapted to sparse modelling techniques.

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