Choosing between Higher Moment Maximum Entropy Models and Its Application to Homogeneous Point Processes with Random Effects

Abstract

In the Bayesian framework, the usual choice of prior in the prediction of homogeneous Poisson processes with random effects is the gamma one. Here, we propose the use of higher order maximum entropy priors. Their advantage is illustrated in a simulation study and the choice of the best order is established by two goodness-of-fit criteria: Kullback–Leibler divergence and a discrepancy measure. This procedure is illustrated on a warranty data set from the automobile industry.

Keywords

• recurrent events
• mixed-Poisson
• the maximum entropy principle
• moment matching
• maximum likelihood estimation
• discrepancy measure
• Kullback–Leibler divergence
• likelihood ratio test
• mean square prediction error