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.

翻译：本研究考虑了独立泊松观测值的联合预测分布，并使用Kullback-Leibler（K-L）损失评估预测分布的性能。本文提出了一类经验贝叶斯预测分布，其表现优于基于Jeffreys先验的贝叶斯预测分布。实验证明，该经验贝叶斯预测分布的K-L风险小于极小极大下界的1.04倍。