Admissibility of a posterior predictive decision rule
This provides a theoretical foundation for Bayesian prediction methods, but it is incremental as it formalizes an existing approach.
The paper tackles the problem of justifying the use of posterior predictive distributions for point predictions in Bayesian models by applying statistical decision theory, resulting in a theoretical justification for this common practice.
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.