Frasian Inference

TL;DR

This paper explores the discrepancies between Bayesian probabilities and confidence levels, highlighting extreme cases and proposing Frasian methods that combine Bayesian and frequentist principles for improved validity.

Contribution

It introduces the concept of Frasian methods, which aim to unify Bayesian and frequentist approaches, and discusses scenarios where these methods are particularly effective.

Findings

Extreme disagreements between Bayesian and confidence levels identified

Frasian methods can achieve frequentist validity in certain cases

Discussion of the potential and challenges of Frasian approaches

Abstract

Don Fraser has given an interesting account of the agreements and disagreements between Bayesian posterior probabilities and confidence levels. In this comment I discuss some cases where the lack of such agreement is extreme. I then discuss a few cases where it is possible to have Bayes procedures with frequentist validity. Such frequentist-Bayesian---or Frasian---methods deserve more attention [arXiv:1112.5582].