|
|
Summary statistics of spatial point processes
Mirtes, Lukáš ; Lechnerová, Radka (advisor) ; Pawlas, Zbyněk (referee)
The paper presents introduction to spatial point processes and their characteristics. The reader is familiar with Poisson point process, which plays fundamental role in the theory of point processes. Basic properties and summary statistics are introruced with nonparametric estimations. The work is concluded by example of the point process including estimations of some charakteristics.
|
|
|
Separability of the intensity function of a Poisson point process
Petráková, Martina ; Dvořák, Jiří (advisor) ; Prokešová, Michaela (referee)
Our main interest in the thesis is Poisson point process and one of its charac- teristics - intensity function. Whenever Poisson process has intensity function, its distribution is uniquely determined by it. Our main goal is to determine how to deduce from observed data whether intensity function is separable. We present a formal test of this hypothesis assuming exponential model of the in- tensity function depending on finite number of parameters. Properties of this test are then examined in a simulation study. 1
|
|
|
Summary statistics of spatial point processes
Mirtes, Lukáš ; Lechnerová, Radka (advisor) ; Pawlas, Zbyněk (referee)
The paper presents introduction to spatial point processes and their characteristics. The reader is familiar with Poisson point process, which plays fundamental role in the theory of point processes. Basic properties and summary statistics are introruced with nonparametric estimations. The work is concluded by example of the point process including estimations of some charakteristics.
|
|
|
Perfect simulation in stochastic geometry
Sadil, Antonín ; Prokešová, Michaela (advisor) ; Beneš, Viktor (referee)
Perfect simulations are methods, which convert suitable Markov chain Monte Carlo (MCMC) algorithms into algorithms which return exact draws from the target distribution, instead of approximations based on long-time convergence to equilibrium. In recent years a lot of various perfect simulation algorithms were developed. This work provides a unified exposition of some perfect simulation algorithms with applications to spatial point processes, especially to the Strauss process and area-interaction process. Described algorithms and their properties are compared theoretically and also by a simulation study.
|
guest ::
