PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Jeffreys vs. Shtarkov Distributions Associated with Some Natural Exponential Families
S.K. Bar-Lev, D. Bshouty, Peter Grünwald and P. Harremoes
Statistical Methodology 2010.

Abstract

Jeffreys and Shtarkov distributions play an important role in universal coding and minimum description length (MDL) inference, two central areas within the field of information theory. It was recently discovered that in some situations Shtarkov distributions exist while Jeffreys distributions do not. To demonstrate some of these situations we consider in this note the class of natural exponential families (NEF’s) and present a general result which enables us to construct numerous classes of infinitely divisible NEF’s for which Shtarkov distributions exist and Jeffreys distributions do not. The method used to obtain our general results is based on the variance functions of such NEF’s. We first present two classes of parametric NEF’s demonstrating our general results and then generalize them to obtain numerous multiparameter classes of the same type.

EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:7580
Deposited By:Peter Grünwald
Deposited On:17 March 2011