Bayes estimation of prediction intervals for a power law process

Abstract

Given the first n successive occurence times from a non-homogeneous Poisson process with a power-law intensity function, Bayes prediction intervals for future observations are derived. A Bayesian approach is compared, via Monte Carlo simulation, with a classical one, taking into account several factors, such as prior information, sample size and true values of process parameters. It is found that the Bayesian procedure generally attains sensibly better performances even when there is little prior information available.