Simultaneous prediction for independent Poisson processes with different durations

Abstract

Simultaneous predictive densities for independent Poisson observables are investigated. The observed data and the target variables to be predicted are independently distributed according to different Poisson distributions parametrized by the same parameter. The performance of predictive densities is evaluated by the Kullback-Leibler divergence. A class of prior distributions depending on the objective of prediction is introduced. A Bayesian predictive density based on a prior in this class dominates the Bayesian predictive density based on the Jeffreys prior.

19 pages

References in corpus (3)

• Improved minimax predictive densities under Kullback--Leibler loss
• From Minimax Shrinkage Estimation to Minimax Shrinkage Prediction
• Asymptotic Properties of Bayesian Predictive Densities When the Distributions of Data and Target Variables are Different

Cited by in corpus (8)

• Bayesian Shrinkage Estimation of Negative Multinomial Parameter Vectors
• Minimax Predictive Density for Sparse Count Data
• Bayesian Estimation of Multinomial Cell Probabilities Incorporating Information from Aggregated Observations
• Bayesian Shrinkage Estimation for Stratified Count Data
• On $\epsilon$-Admissibility in High Dimension and Nonparametrics
• Shrinkage priors for nonparametric Bayesian prediction of nonhomogeneous Poisson processes
• Bayesian Shrinkage Approaches to Unbalanced Problems of Estimation and Prediction on the Basis of Negative Multinomial Samples
• Bayesian Estimation for the Multivariate Hypergeometric Distribution Incorporating Information from Aggregated Observations