Admissibility of a posterior predictive decision rule

TL;DR

This paper uses statistical decision theory to justify the use of posterior predictive distributions for making point predictions in Bayesian models, emphasizing their admissibility.

Contribution

It provides a decision-theoretic justification for the admissibility of posterior predictive decision rules in Bayesian inference.

Findings

Posterior predictive decision rules are admissible under certain conditions.

Decision theory supports the use of posterior predictive distributions for point predictions.

The approach clarifies the theoretical foundations of Bayesian prediction methods.

Abstract

Recent decades have seen an interest in prediction problems for which Bayesian methodology has been used ubiquitously. Sampling from or approximating the posterior predictive distribution in a Bayesian model allows one to make inferential statements about potentially observable random quantities given observed data. The purpose of this note is to use statistical decision theory as a basis to justify the use of a posterior predictive distribution for making a point prediction.