  We present a general statistical methodology for analysing a Laguerre
tessellation data set viewed as a realization of a marked point process model.
In the first step, for the points we use a nested sequence of multiscale
processes which constitute a flexible parametric class of pairwise interaction
point process models. In the second step, for the marks/radii conditioned on
the points we consider various exponential family models where the canonical
sufficient statistic is based on tessellation characteristics. For each step
parameter estimation based on maximum pseudolikelihood methods is tractable.
Model checking is performed using global envelopes and corresponding tests in
the first step and by comparing observed and simulated tessellation
characteristics in the second step. We apply our methodology for a 3D Laguerre
tessellation data set representing the microstructure of a polycrystalline
metallic material, where simulations under a fitted model may substitute
expensive laboratory experiments.
