Simultaneous Prediction of Independent Poisson Observables

• Published in: The Annals of statistics Vol. 32; no. 4; pp. 1744 - 1769
• Main Author: Komaki, Fumiyasu
• Format: Journal Article
• Language: English
• Published: Hayward, CA Institute of Mathematical Statistics 01-08-2004; The Institute of Mathematical Statistics
• Subjects: 62C15; 62F15; Admissibility; Bayes estimators; Bayesian analysis; Coding theory; Distribution; Distribution theory; Entropy; Estimators; Exact sciences and technology; Inference from stochastic processes; time series analysis; Infinity; Integrands; Jeffreys prior; Kullback–Leibler divergence; Mathematical independent variables; Mathematical models; Mathematics; Maximum likelihood estimation; Prediction; predictive distribution; Probability and statistics; Probability theory and stochastic processes; Random variables; Sciences and techniques of general use; shrinkage prior; Statistics; Stochastic processes; Studies; Bayes estimation; Statistical method; Distribution function; Poisson distribution; Prior distribution; Predictive distribution
• ISSN: 0090-5364; 2168-8966
• DOI: 10.1214/009053604000000445

Simultaneous predictive distributions for independent Poisson observables are investigated. A class of improper prior distributions for Poisson means is introduced. The Bayesian predictive distributions based on priors from the introduced class are shown to be admissible under the Kullback-Leibler loss. A Bayesian predictive distribution based on a prior in this class dominates the Bayesian predictive distribution based on the Jeffreys prior.