What is the question that MaxEnt answers? A probabilistic interpretation

TL;DR

This paper provides a probabilistic interpretation of MaxEnt, showing it as an asymptotic case of finding the most probable frequency vector under a uniform prior, based on the Boltzmann-Wallis-Jaynes argument.

Contribution

It offers a new probabilistic perspective on MaxEnt, connecting it to the likelihood of frequency vectors under a uniform prior, and elaborates on the multiplicity argument.

Findings

MaxEnt is an asymptotic case of maximum probability frequency vectors.

The Boltzmann-Wallis-Jaynes argument underpins the MaxEnt principle.

MaxEnt corresponds to the most probable frequency distribution under a uniform prior.

Abstract

The Boltzmann-Wallis-Jaynes' multiplicity argument is taken up and elaborated. MaxEnt is proved and demonstrated to be just an asymptotic case of looking for such a vector of absolute frequencies in a feasible set, which has maximal probability of being generated by a uniform prior generator/pmf.