Measure Selection: Notions of Rationality and Representation Independence

TL;DR

This paper critically examines measure selection methods, questioning the dominance of entropy maximization and proposing alternative principles and methods for representation-independent measure selection.

Contribution

It introduces the likelihood of evidence principle as an alternative to entropy maximization and reviews a method for achieving representation independence in measure selection.

Findings

Entropy maximization's dominance is questioned.

Likelihood of evidence principle is proposed as an alternative.

A method for representation-independent measure selection is discussed.

Abstract

We take another look at the general problem of selecting a preferred probability measure among those that comply with some given constraints. The dominant role that entropy maximization has obtained in this context is questioned by arguing that the minimum information principle on which it is based could be supplanted by an at least as plausible "likelihood of evidence" principle. We then review a method for turning given selection functions into representation independent variants, and discuss the tradeoffs involved in this transformation.