PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

An algorithmic and a geometric characterizatoin of coarsening at random.
Richard Gill and Peter Grünwald
(2005) Math ArXiv, Math ArXiV, section statistics, math.ST/0510276.


We show that the class of conditional distributions satisfying the Coarsening at Random (CAR) property has a simple algorithmic description based on randomized uniform multicovers, which are combinatorial objects generalizing the notion of partition of a set. The maximum needed {\em height\/} of the multicovers is exponential in the number of points in the sample space. This algorithmic characterization stems from a geometric interpretation of the set of CAR distributions as a convex polytope and a characterization of its extreme points. The hierarchy of CAR models defined in this way can be useful in parsimonious statistical modelling of CAR mechanisms.

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EPrint Type:Other
Additional Information:Item under submission but this version is available at the Math ArXiV
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
ID Code:319
Deposited By:Peter Grünwald
Deposited On:28 November 2005