National Repository of Grey Literature 719 records found  previous11 - 20nextend  jump to record: Search took 0.01 seconds. 
Point processes on networks
Zahrádková, Petra ; Beneš, Viktor (advisor) ; Dvořák, Jiří (referee)
The aim of this master thesis is to develop the background for point processes on both the linear network and the planar network in R3 . The linear, planar network is formed by the system of edges, faces of a 3D tessellation, respectively. Using the Gibbs-Laguerre tessellation model we can investigate the case of a regular or irregular tessellation. We consider cluster and hard core point processes and we compare two types of distances between points, the Euclidean distance and the shortest path distance within the net- work. The algorithms for simulation of point processes on both networks are developed. Using the simulated realizations of point processes we estimate some functional summary characteristics. Based on plotted graphs of these estimates, the influence of the choice of tessellations, point process models and distances is discussed. 1
Computations of Laguerre tessellations with given cell volumes
Kornijčuk, Oleksandr ; Beneš, Viktor (advisor) ; Dvořák, Jiří (referee)
Given a finite set of pairs in Rd ×R, nuclei and weights, Laguerre tessellations allow us to subdivide Euclidean space Rd into finitely many polyhedral cells using the power dis- tance. We are interested in the problem of finding weights so that the Laguerre cells have prescribed volumes and nuclei. Our primary aim is to present the theoretical background leading to the problem's solution. Here we complete some proofs that are shortened in the literature, while other theorems are cited. Then, we demonstrate two own computer programs and the corresponding numerical results. First, we compute the desired set of weights that generates the Laguerre tessellation with prescribed cell volumes and apply it to a unit cube in R3 . The application of this method relies on the Barzilai-Borwein gradient descent and Voro++ library, which computes the volumes of cells in each itera- tion. Furthermore, an iterative approach approximates a centroidal Laguerre tessellation, where the nuclei coincide with the centroids of Laguerre cells. 1
Non-orphan cluster point processes
Hájková, Eliška ; Dvořák, Jiří (advisor) ; Beneš, Viktor (referee)
In this work we introduce some basic concepts from the theory of spatial point pro- cesses and two methods of estimation of the parametres for Thomas process. Firstly the method of minimum contrast, that is used for situations when we do not know the position of parent points and secondly our proposed method using information about the parent points location. Using simulations in program R, we find out that our method estima- ted mentioned parameters better considering the relative bias and relative mean squared error. Subsequently, we estimate the parameters of the real data using both methods. Fi- nally we test by Global Envelope Test, whether our data match Thomas process with para- meters estimated from data with mentioned methods. For the combinations of parameters obtained by discussed methods we do not reject the hypothesis. 1
Spatial epidemiology
Jalovcová, Adéla ; Dvořák, Jiří (advisor) ; Pawlas, Zbyněk (referee)
This work deals with spa al sta s cs methods that are suitable for analysing spa al epidemiological data. The work presents tests of spa al autocorrela on and applies them on data of the number of people infected by Covid 19. The main part of the work is Bayesian modelling of epidemiological data using Integrated Nested Laplace Approxima ons. We summarise the main principles of this method and present a chosen model for given data. Besides the spa al aspect of the data, the work shows how to incorporate other risk factors into the model and how to make the model spa o-temporal. Furthermore the work applies the model on the data and tests the suitability of the model with a global envelope test.
EM algorithm for truncated Gaussian mixtures
Nguyenová, Adéla ; Dvořák, Jiří (advisor) ; Nagy, Stanislav (referee)
The expectation-maximization iterative algorithm is widely used in parameter estimation when dealing with missing information. Such a situation can naturally arise when we observe the data of our interest on a bounded observation window. This thesis focuses on the application of the EM algorithm for truncated Gaussian mixtures and compares the proposed algorithm with the approach in a previously published article, see Lee and Scott [2012], where it uses a heuristic simplification and is not sufficiently supported mathematically. We also compare the behavior of the proposed algorithm with the procedure from the article in a series of simulated experiments, as well as in analyzing a real dataset. We also provide Python implementation of the EM algorithm for truncated Gaussian mixtures.
Parametric estimation of the intensity function of point processes
Rybín, Jan ; Dvořák, Jiří (advisor) ; Prokešová, Michaela (referee)
The thesis introduces spatial point processes. Particularly, it focuses on Poisson process, Thomas process and intensity function, which describes those two processes. The main focus is put on processes that depend on an unknown parameter. It is shown that in order to find an estimate of the unknown parameter even for general processes, it is reasonable to use maximum likelihood function derived from Poisson processes. All new terminology is explained in detail with the help of simple examples. The new terminology is then used in simulation studies that compare qualities of estimates in different statistical models. 1
Point processes on the sphere
Svoboda, Willy ; Dvořák, Jiří (advisor) ; Seitl, Filip (referee)
A point process can be easily described as a random locally finite set. For example, we can model locations of arbitrary events in a city or in the world such as earthquake epicenter locations. In this thesis, we introduce basic types of point processes in a Euc- lidean space and on a sphere, describe what situations can be modelled by them, define basic properties, and lay down theoretical groundwork for the K-function (and its modi- fications for marked point processes). The main goal of this thesis is to introduce marked point processes on a sphere and to give theoretical framework, whereas the marks will give us another nontrivial information about the points, which we want to study further. In the conclusion of the thesis, we concern ourselves with testing whether those marks are mutually independent. We apply Monte Carlo permutation test using mark-weighted K-function for marked point processes on a sphere. 1
Operational risk and marked Poisson process
Váchová, Karla ; Pešta, Michal (advisor) ; Dvořák, Jiří (referee)
The subject of this bachelor thesis entitled "Operational risk and marked Poisson process" is the modelling of operational risk using marked Poisson process. The Poisson process is a type of a point process that models randomly distributed points on some underlying space. Because of its mathematical properties, it is a quite frequently used model in biology, astronomy, ecology or economics, for example. This bachelor thesis describes its basic properties and uses the marked Poisson process to model loss frequency and severity belonging to bank's operational risk. 1
Estimation of the K-function of a point process using global normalization
Funková, Veronika ; Dvořák, Jiří (advisor) ; Prokešová, Michaela (referee)
Point processes are random local finite sets of points in a space that are used for mod- elling and subsequent spatial data analysis. Same of their useful characteristics are the pair correlation function and also the K-function, which describe point interactions with respect to the distance between points. There are several ways to include informa- tion about the non-constant intensity function in the estimates of these characteristics for inhomogeneous processes. In the older estimate, we use information about a value of the intensity function only in places where the process points are located. However, the new estimate works with a value of the intensity function within the whole observation window. In this thesis we focus on the comparison of these two estimates. In the third chapter we theoretically present these estimates and in the fourth chapter we compare their behaviour based on simulations of 8 point process models, while finding the optimal value of bandwidth for their kernel estimates. 1
Point processes of objects with random lifetime
Kulla, Filip ; Dvořák, Jiří (advisor) ; Beneš, Viktor (referee)
The thesis deals with point processes of objects with random lifetime. The form of the likelihood function of an observed spatial-temporal pattern with random lifetimes is derived, where the formula is subsequently generalised to the case of censored life- times. Moreover, some simple parametric models are introduced and conditions under which they are non-explosive are derived. In addition, aspects of our implementation of the algorithm which generates a realisation of a given spatial-temporal point process with random lifetimes and of the likelihood-based estimation are discussed. The thesis contains a simulation study in which the use of the (partial) likelihood on simulated data is demonstrated and properties of resulting estimates are discussed. Furthermore, it contains an application of the partial likelihood to the real data, where the question of interest is the spatial dynamics of propagation of an observed population of flowers. 1

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