Some cautionary tales about Bayesian predictive inference

2026-07-21

AI Summary

This study clarifies two common misconceptions in Bayesian predictive inference concerning the modeling of data-generating mechanisms and the role of asymptotic exchangeability. By constructing counterexamples and drawing on exchangeability theory, the authors systematically examine how misspecification of the data-generating process and overreliance on asymptotic exchangeability in practice can lead to erroneous predictive conclusions. The analysis demonstrates that these misunderstandings can substantially compromise the validity of Bayesian predictions, thereby deepening the understanding of the foundational assumptions underlying Bayesian inference. The findings offer crucial theoretical guidance for the appropriate application of Bayesian methods, emphasizing the need for careful consideration of both modeling assumptions and the limits of exchangeability-based justifications.

Abstract

Two misunderstandings, frequently arising in Bayesian predictive inference, are discussed. The first deals with the data generating mechanism, while the second consists in overestimating the role played by asymptotic exchangeability. Some consequences of such misunderstandings are highlighted through examples.

Problem

• Bayesian predictive inference
• data generating mechanism
• asymptotic exchangeability
• misunderstandings

Innovation

• Bayesian predictive inference
• data generating mechanism
• asymptotic exchangeability
• misunderstandings
• cautionary tales