SMML estimators for exponential families with continuous sufficient statistics
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The minimum message length principle is an information theoretic criterion that links data compression with statistical inference. This paper studies the strict minimum message length (SMML) estimator for d-dimensional exponential families with continuous sufficient statistics, for all d > 1. The partition of an SMML estimator is shown to consist of convex polytopes (i.e. convex polygons when d=2) which can be described explicitly in terms of the assertions and coding probabilities. While this result is known, we give a new proof based on the calculus of variations, and this approach gives some interesting new inequalities for SMML estimators. We also use this result to construct an SMML estimator for a 2-dimensional normal random variable with known variance and a normal prior on its mean.
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