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Non‐parametric Bayesian Estimation of a Spatial Poisson Intensity
Author(s) -
Heikkinen Juha,
Arjas Elja
Publication year - 1998
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00114
Subject(s) - mathematics , random field , point process , smoothing , bayesian probability , markov random field , piecewise , poisson distribution , voronoi diagram , intensity (physics) , statistics , parametric statistics , algorithm , artificial intelligence , mathematical analysis , image segmentation , computer science , geometry , segmentation , physics , quantum mechanics
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.