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The assignment of adequate probabilities to the basic outcomes of some random experiment under consideration is a prerequisite of a probabilistic description. The maximum entropy principle of Statistical Mechanics solves this problem by stating that among all probability distributions that satisfy some given constraints the one of maximum Boltzmann-Gibbs-Shannon entropy must be chosen. Being an indisputable principle of Statistical Mechanics, its status outside physics as a general method of statistical inference is less clear. We present a foundation of the maximum entropy principle that is based on probabilistic arguments. It deliberately avoids reference to notions of information and it does not appeal to physically motivated properties of entropy. This is achieved by formalizing probability assignment as a certain symmetric, continuous mapping that additionally satisfies a condition of self-consistency. We show that any such mapping can be expressed as a variational principle, i.e. as a generalized maximum entropy principle with an a priori unspecified entropy function. Adding a condition of statistical independence, an earlier result of Shore and Johnson shows that the entropy function must be essentially the standard Boltzmann-Gibbs-Shannon entropy.

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Dr. Rochus Klesse, University of Cologne, Institute for Theoretical Physics
Seminarraum Theoretische Physik
Contact: not specified