Random forests for homogeneous and non-homogeneous Poisson processes with excess zeros

We propose a general hurdle methodology to model a response from a homogeneous or a non-homogeneous Poisson process with excess zeros, based on two forests. The first forest in the two parts model is used to estimate the probability of having a zero. The second forest is used to estimate the Poisson parameter(s), using only the observations with at least one event. To build the trees in the second forest, we propose specialized splitting criteria derived from the zero truncated homogeneous and non-homogeneous Poisson likelihood. The particular case of a homogeneous process is investigated in details to stress out the advantages of the proposed method over the existing ones. Simulation studies show that the proposed methods perform well in hurdle (zero-altered) and zero-inflated settings, for both homogeneous and non-homogeneous processes. We illustrate the use of the new method with real data on the demand for medical care by the elderly.