  In this paper we provide theoretical support for the so-called "Sigmoidal
Gaussian Cox Process" approach to learning the intensity of an inhomogeneous
Poisson process on a $d$-dimensional domain. This method was proposed by Adams,
Murray and MacKay (ICML, 2009), who developed a tractable computational
approach and showed in simulation and real data experiments that it can work
quite satisfactorily. The results presented in the present paper provide
theoretical underpinning of the method. In particular, we show how to tune the
priors on the hyper parameters of the model in order for the procedure to
automatically adapt to the degree of smoothness of the unknown intensity and to
achieve optimal convergence rates.
