PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

An Algorithmic and a Geometric Characterization of Coarsening at Random
Richard Gill and Peter Grünwald
Annals of Statistics 2007.


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:Article
Additional Information:The file is a preliminary version that was placed on the math arxiv. The final version will look slightly different.
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Theory & Algorithms
ID Code:2740
Deposited By:Peter Grünwald
Deposited On:22 November 2006