A Spline-based Method for Modelling and Generating a Nonhomogeneous Poisson Process

This paper presents a spline-based input modelling method for inferring the intensity function of a nonhomogeneous Poisson process (NHPP) given arrival-time observations. A simple method for generating arrivals from the resulting intensity function is also presented. Splines are a natural choice for modelling intensity functions as they are smooth by construction, and highly flexible. Although flexibility is an advantage in terms of reducing the bias with respect to the true intensity function, it can lead to overfitting. Our method is therefore based on maximising the penalised NHPP log-likelihood, where the penalty is a measure of rapid changes in the spline-based representation. An empirical comparison of the spline-based method against two recently developed input modelling techniques is presented, along with an illustration of the method given arrivals from a real-world accident and emergency (A&E) department.