  A Neyman-Scott process is a special case of a Cox process. The latent and
observable stochastic processes are both Poisson processes. We consider a deep
Neyman-Scott process in this paper, for which the building components of a
network are all Poisson processes. We develop an efficient posterior sampling
via Markov chain Monte Carlo and use it for likelihood-based inference. Our
method opens up room for the inference in sophisticated hierarchical point
processes. We show in the experiments that more hidden Poisson processes brings
better performance for likelihood fitting and events types prediction. We also
compare our method with state-of-the-art models for temporal real-world
datasets and demonstrate competitive abilities for both data fitting and
prediction, using far fewer parameters.
