Shrinkage priors for nonparametric Bayesian prediction of nonhomogeneous Poisson processes

Abstract

We consider nonparametric Bayesian estimation and prediction for nonhomogeneous Poisson process models with unknown intensity functions. We propose a class of improper priors for intensity functions. Nonparametric Bayesian inference with kernel mixture based on the class improper priors is shown to be useful, although improper priors have not been widely used for nonparametric Bayes problems. Several theorems corresponding to those for finite-dimensional independent Poisson models hold for nonhomogeneous Poisson process models with infinite-dimensional parameter spaces. Bayesian estimation and prediction based on the improper priors are shown to be admissible under the Kullback--Leibler loss. Numerical methods for Bayesian inference based on the priors are investigated.

References in corpus (6)

• Improved minimax predictive densities under Kullback--Leibler loss
• Admissible predictive density estimation
• Asymptotics for posterior hazards
• Simultaneous prediction for independent Poisson processes with different durations
• Asymptotic minimax risk of predictive density estimation for non-parametric regression
• Bayesian Shrinkage Estimation of Negative Multinomial Parameter Vectors