A spline function method for modelling and generating a nonhomogeneous poisson process

This paper presents a spline-based input modelling method for inferring the rate function of nonhomogeneous Poisson process (NHPP) given arrival-time observations and simple generating arrivals from resulting function. Splines are natural choice functions as they smooth by construction, highly flexible. Although flexibility is an advantage in terms reducing bias with respect to true function, it can lead overfitting. Our therefore based on maximising penalised NHPP log-likelihood, where penalty measure rapid changes representation. A controlled empirical comparison against two recently developed techniques presented considering recovery propagation error, performance methods data that under or over-dispersed process.