NONPARAMETRIC BAYESIAN-ESTIMATION OF A SPATIAL POISSON INTENSITY

A method introduced by Arjas & Gasbarra (1994) and later modified by A rjas & Heikkinen (1997) for the non-parametric Bayesian estimation of an intensity on the real line is generalized to cover spatial processe s. The method is based on a model approximation where the approximatin g intensities have the structure of a piecewise constant function. Ran dom step functions on the plane are generated using Voronoi tessellati ons of random point patterns, Smoothing between nearby intensity value s 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.