A Neyman-Scott process is a special case of a Cox process. The latent andobservable stochastic processes are both Poisson processes. We consider adeep Neyman-Scott process in this paper, for which the building componentsof a network are all Poisson processes. We develop an efficient posteriorsampling via Markov chain Monte Carlo and use it for likelihood-basedinference. Our method opens up room for the inference in sophisticatedhierarchical point processes. We show in the experiments that more hiddenPoisson processes brings better performance for likelihood fitting andevents types prediction. We also compare our method with state-of-the-artmodels for temporal real-world datasets and demonstrate competitiveabilities for both data fitting and prediction, using far fewer parameters.