Nearly minimax empirical Bayesian prediction of independent Poisson observables

TL;DR

This paper develops empirical Bayesian predictive distributions for independent Poisson variables, outperforming traditional Bayesian methods by achieving lower Kullback-Leibler risk and approaching minimax optimality.

Contribution

It introduces a new class of empirical Bayesian predictors that dominate Jeffreys prior-based Bayesian predictors in Poisson models.

Findings

Empirical Bayesian predictors have K-L risk less than 1.04 times the minimax lower bound.

The proposed predictors outperform Bayesian predictors based on Jeffreys prior.

The method provides nearly minimax optimal prediction for Poisson observables.

Abstract

In this study, simultaneous predictive distributions for independent Poisson observables were considered and the performance of predictive distributions was evaluated using the Kullback-Leibler (K-L) loss. This study proposes a class of empirical Bayesian predictive distributions that dominate the Bayesian predictive distribution based on the Jeffreys prior. The K-L risk of the empirical Bayesian predictive distributions is demonstrated to be less than 1.04 times the minimax lower bound.