Measure Selection: Notions of Rationality and Representation Independence
This work addresses foundational issues in probability theory and statistics, offering an incremental challenge to established methods for measure selection.
The paper questions the dominance of entropy maximization for selecting probability measures under constraints by proposing an alternative 'likelihood of evidence' principle, and reviews a method to make selection functions representation independent while discussing tradeoffs.
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.