Stereological analysis of the spatial Poisson–Voronoi tessellation

Summary Stereological model tests and parameter estimators for the spatial Poisson–Voronoi tessellation are discussed. The tests aim to discriminate the Poisson–Voronoi tessellation from more regular or more irregular tessellations. The power of the model tests under some special parametric alternative hypotheses is investigated by simulation. Among the tests considered, the most powerful test is based on the variance of the section cell areas. Various stereological estimators for the model parameter of the spatial Poisson–Voronoi tessellation are compared with respect to their bias and variance by means of a Monte–Carlo study. Formulae are given for variance prediction. An estimator based on vertex counting is found to be the best. Robustness is investigated by applying the estimators to Voronoi tessellations generated by other point process models.