B0541
Title: Bayesian nonparametric intensity estimation for inhomogeneous point processes with covariates
Authors: Matteo Giordano - University of Turin (Italy) [presenting]
Abstract: Bayesian nonparametric estimation of the intensity function of a spatial Poisson point process is studied, in the case where the intensity depends on covariates and a single observation of the process is available. The presence of covariates allows borrowing information from faraway locations in the domain, enabling consistent estimation in the growing domain asymptotics. In particular, posterior concentration rates are derived under both global and local losses. The global rates are obtained under conditions on the prior distribution resembling those in the well-established theory of Bayesian nonparametric, here combined with suitable concentration inequalities for stationary processes to control certain random covariates-dependent losses. The local rates are instead derived with an ad-hoc analysis, exploiting recent advances in the theory of Polya-tree-like priors.
