Non-parametric Bayesian Estimation of a Spatial Poisson Intensity

A method introduced by Arjas & Gasbarra (1994) and later modified by Arjas & Heikkinen (1997) for the non-parametric Bayesian estimation of an intensity on the real line is generalized to cover spatial processes. The method is based on a model approximation where the approximating intensities have the structure of a piecewise constant function. Random step functions on the plane are generated using Voronoi tessellations of random point patterns. Smoothing between nearby intensity values is applied by means of a Markov random field prior in the spirit of Bayesian image analysis. The performance of the method is illustrated in examples with both real and simulated data.