### Tomas Mrkvicka, Ph.D.

tel.: +420 387 772 700

e-mail: mrkvicka.toma@gmail.com

### Projects

**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
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