Gibbs conditioning extended, Boltzmann conditioning introduced

TL;DR

This paper extends classical probabilistic principles to cases with multiple optimal distributions, providing a theoretical foundation for the MaxProb method and discussing the relation between REM and MaxEnt.

Contribution

It introduces the ICET and EGCP principles for non-unique REM distributions, extending the Gibbs Conditioning Principle and providing a probabilistic basis for MaxProb.

Findings

Extended Gibbs Conditioning Principle (EGCP) for non-unique cases

Probabilistic justification for MaxProb method

Introduction of mu-projection variants

Abstract

Conditional Equi-concentration of Types on I-projections (ICET) and Extended Gibbs Conditioning Principle (EGCP) provide an extension of Conditioned Weak Law of Large Numbers and of Gibbs Conditioning Principle to the case of non-unique Relative Entropy Maximizing (REM) distribution (aka I-projection). ICET and EGCP give a probabilistic justification to REM under rather general conditions. mu-projection variants of the results are introduced. They provide a probabilistic justification to Maximum Probability (MaxProb) method. 'REM/MaxEnt or MaxProb?' question is discussed, briefly. Jeffreys Conditioning Principle is mentioned.