Prediction intervals for the Poisson model with applications to Atlantic storms data

In this research we construct prediction intervals for a Poisson process using both frequentist and Bayesian approaches. A general algorithm for the whole class of discrete distribution from the exponential family is introduced. The relationship between prediction limits derived using Bayesian approach when a noninformative prior is assumed on the parameter with limits derived using frequentist approach is taken under special consideration. As an application, the exact prediction limits for the number of tropical storms occurring during some time scale in the future are constructed based on a Poisson modeling; both frequentist and Bayesian approaches are considered. Simulation techniques and bootstrap methods are performed to assess the prior distribution.