Discussion of "On the Birnbaum Argument for the Strong Likelihood Principle"

TL;DR

This paper discusses how fiducial distributions serve as an example of an inference method that violates the Strong Likelihood Principle but adheres to the Weak Conditionality Principle, highlighting nuances in statistical inference principles.

Contribution

It clarifies the relationship between fiducial distributions and foundational likelihood principles, challenging assumptions about their compatibility.

Findings

Fiducial distributions violate the Strong Likelihood Principle.

Fiducial distributions satisfy the Weak Conditionality Principle.

The discussion clarifies foundational aspects of statistical inference.

Abstract

In this discussion we demonstrate that fiducial distributions provide a natural example of an inference paradigm that does not obey Strong Likelihood Principle while still satisfying the Weak Conditionality Principle. [arXiv:1302.7021]