Tomas Mrkvicka

tel.: +420 387 772 700
e-mail: mrkvicka.toma@gmail.com

Estimation of Intrinsic Volumes in 2D - T. Mrkvicka, T. Kaiser - The program for estimating intrinsic volumes densities in 2D is available here. A new method of estimation of intrinsic volume densities for a stationary random closed set X with values in the extended convex ring is introduced. The local Steiner formula is applied to the closure of the complement of the parallel set for n different radii and, by solving a linear regression model, estimates of the intrinsic volume densities of the parallel set are obtained, which are used as approximations of those of X itself.
Test of the random set model hypothesis - T. Mrkvicka, T. Kaiser - The program for estimating intrinsic volumes densities in 2D, which are prepared for the test of the random set model hypothesisis, is available here. A new method of testing the random closed set model hypothesis (for example: the Boolean model hypothesis) for a stationary random closed set Xi with values in the extended convex ring is introduced. The method is based on the estimating of the intrinsic volumes densities of the epsilon-parallel sets to Xi and comparing them with its envelopes produced from simulations of the model given by the tested hypothesis.
Estimation of Intrinsic Volumes in 3D - T. Mrkvicka, T. Kaiser - The program for estimating intrinsic volumes densities in 3D is available here.
Simulation study on Point Processes Testing: Diploma thesis by Taras Perevorskyy