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National Repository of Grey Literature 2 records found  Search took 0.01 seconds. 
Normal approximation for statistics of Gibbs point processes
 Maha, Petr ; Beneš, Viktor (advisor) ; Dvořák, Jiří (referee)
In this thesis, we deal with finite Gibbs point processes, especially the processes with densities with respect to a Poisson point process. The main aim of this work is to investigate a four-parametric marked point process of circular discs in three dimensions with two and three way point interactions. In the second chapter, our goal is to simulate such a process. For that purpose, the birth- death Metropolis-Hastings algorithm is presented including theoretical results. After that, the algorithm is applied on the disc process and numerical results for different choices of parameters are presented. The third chapter consists of two approaches for the estimation of parameters. First is the Takacs-Fiksel estimation procedure with a choice of weight functions as the derivatives of pseudolikelihood. The second one is the estimation procedure aiming for the optimal choice of weight functions for the estimation in order to provide better quality estimates. The theoretical background for both of these approaches is derived as well as detailed calculations for the disc process. The numerical results for both methods are presented as well as their comparison. 1
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Modelling of segment process in the plane
 Pultar, Milan ; Beneš, Viktor (advisor) ; Pawlas, Zbyněk (referee)
We consider a finite planar segment process in a circle, having a density with respect to the Poisson process. This density involves unknown parameters and a reference length distribution which is not observed. The aim is to estimate these quantities semiparametrically. The segment process is inhomogeneous, but it is isotropic. Combining the relation between the observed and reference length distribution and the maximum pseudolikelihood method we suggest an estimation procedure. Its properties (bias and variability) are investigated in a simulation study. In the last part we present two more complex models. The motivation is to model stress fibers observed in cultured stem cells.
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