Bayes Linear Estimators of the Intensity Function of the Nonstationary Poisson Process

Abstract

A Bayesian approach is taken to the problem of estimating the intensity function of a nonstationary Poisson process. The intensity function, Λ(t), − T < t < T, is a priori a second-order stochastic process. Estimators are found which minimize among, respectively, the class of step functions, the class of moving averages, and a class of linear estimators. An approximation for large T to the last estimator is found. These estimators are compared in a numerical example involving the wildcat oilwell discovery process in Alberta for the years 1953–1971.

Key Words:

• Poisson processes
• Bayes linear estimators
• Filtering
• Poisson signals
• Doubly stochastic processes
• Point processes