Smooth flexible models of nonhomogeneous poisson processes using one or more process realizations

We develop and evaluate a semiparametric method to estimate the mean-value function of a nonhomogeneous Poisson process (NHPP) using one or more process realizations observed over a fixed time interval. To approximate the mean-value function, the method exploits a specially formulated polynomial that is constrained in least-squares estimation to be nondecreasing so the corresponding rate function is nonnegative and smooth (continuously differentiable). An experimental performance evaluation for two typical test problems demonstrates the method¿s ability to yield an accurate fit to an NHPP based on a single process realization. A third test problem shows how the method can estimate an NHPP based on multiple realizations of the process.