Admissibility of a posterior predictive decision rule

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.