Discussion of Martingale Posterior Distributions by E. Fong, C. Holmes, and S. G. Walker

TL;DR

This paper discusses the relationship between martingale posterior distributions, the frequentist bootstrap, and the stick-breaking process, providing theoretical insights and commentary on prior research.

Contribution

It offers a theoretical commentary linking martingale posteriors with bootstrap methods and the stick-breaking process, expanding understanding of their connections.

Findings

Established a theorem relating bootstrap and stick-breaking process

Provided insights into martingale posterior distributions

Commented on previous research in the field

Abstract

In this discussion note, we respond to the fascinating paper "Martingale Posterior Distributions" by E. Fong, C. Holmes, and S. G. Walker with a couple of comments. On the basis of previous research, a theorem is stated regarding the relationship between frequentist bootstrap and stick-breaking process.