Priors for the Bayesian star paradox

TL;DR

This paper extends the Bayesian star paradox to a broader range of prior distributions, including irregular and discontinuous ones, demonstrating its wider applicability beyond previously studied cases.

Contribution

It generalizes the Bayesian star paradox to include less regular and discontinuous prior distributions, broadening the understanding of its occurrence.

Findings

The paradox occurs with a wider class of priors.

Discontinuous priors can also produce the paradox.

The results expand the theoretical scope of the paradox.

Abstract

We show that the Bayesian star paradox, first proved mathematically by Steel and Matsen for a specific class of prior distributions, occurs in a wider context including less regular, possibly discontinuous, prior distributions.