Fast and scalable non-parametric Bayesian inference for Poisson point processes

We study the problem of non-parametric Bayesian estimation of the intensity function of a Poisson point process. The observations are n independent realisations of a Poisson point process on the interval [0,T]. We propose two related approaches. In both approaches we model the intensity function as piecewise constant on N bins forming a partition of the interval [0,T]. In the first approach the coefficients of the intensity function are assigned independent gamma priors, leading to a closed form posterior distribution. On the theoretical side, we prove that as n→∞, the posterior asymptotically concentrates around the "true", data-generating intensity function at an optimal rate for h-Hölder regular intensity functions (0