
Analysis of the impact of cultural and political factors on European integration assessment based on public opinion of selected countries
Bročková, Klaudia ; Jelen, Libor (advisor) ; Anděl, Jiří (referee)
In the past few years, European integration has often encountered resistance from individual countries when deepening cooperation in specific European policies. The different sociocultural, political and historical backgrounds of the individual member states prove to be potentially problematic, and it appears there is also great diversity in the attitudes of European public opinion. The presented work deals with the issue of the perception of European integration in EU countries, with the aim of evaluating to what extent the current attitude of public opinion towards European integration can be explained by the culturalpolitical dimension of attitudes. Factor and regression analysis were used to examine the relationships and measure the significance of the impacts. The culturalpolitical dimension  represented by factors such as political assessment, immigration assessment, religion and traditionalism, and emotional attachment  explains, based on the results of the regression analysis, on average 22 % of the overall attitude towards European integration. However, the values differ significantly in the conditions of individual countries. The results also questioned the attachment to the national country or the importance of religiosity and traditionalism, as important predictors in rejecting...


Success runs in series of Bernoulli trials
Mach, Tibor ; Anděl, Jiří (advisor) ; Dvořák, Marek (referee)
This work is focused on selected probability characteristics of runs in a sequence of Bernoulli trials and on some randomness tests based on these runs. Based on Markov chains, an explicit formula is derived for the probability that the first success run of a lenght $k$ in a sequence of independent Bernoulli trials occurs in the $n$th trial and other formulas for this probability are mentioned. Furthermore, approximations of the exact value of this probability (particularly the Feller approximation), bounds of these approximations, and their numeric relations are examined. Lastly, a test of randomness based on the lenght of the longest run in a sequence of $n$ Bernoulli trials and a test based on the total amount of runs are derived.

 

Prediction of transformed time series
Polák, Tomáš ; Anděl, Jiří (advisor) ; Jarušková, Daniela (referee)
The aim of this thesis is to find prediction for nonlinear transformation of time series. First, under certain assumptions regarding the original time series, the autocovariance function and spectral density of the transformed time series are studied. General theorems are applied to concrete ARMA processes. Then general formulas for predictions of the transformed time series, which do not require knowledge of the autocovariance function of the transformed series nor its spectral density are presented. These formulas are applied to three concrete transformations and explicit formulas for ARMA processes are derived. Three types of predictions (optimal, naive and linear) are compared in the terms of proportional increase of mean square prediction error. Explicit formulas for ARMA processes are verified by a simulation.


Nonlinearity in time series models
Kalibán, František ; Anděl, Jiří (advisor) ; Zvára, Karel (referee)
The thesis concentrates on property of linearity in time series models, its definitions and possibilities of testing. Presented tests focus mainly on the time domain; these are based on various statistical methods such as regression, neural networks and random fields. Their implementation in R software is described. Advantages and disadvantages for tests, which are implemented in more than one package, are discussed. Second topic of the thesis is additivity in nonlinear models. The definition is introduced as well as tests developed for testing its presence. Several test (both linearity and additivity) have been implemented in R for purposes of simulations. The last chapter deals with application of tests to real data. 1


Introduction to Bayesian Data Analysis
Štádlerová, Kateřina ; Kulich, Michal (advisor) ; Anděl, Jiří (referee)
of the bachelor's thesis Title: Introduction to Bayesian Data Analysis Author: Kateřina Štádlerová Department: Department of Probability and Mathematical Statistics Supervisor: doc. Mgr. Michal Kulich, Ph.D., Department of Probability and Mathematical Statistics Abstract: The paper deals with basic principles of Bayesian methods. These me thods have very broad range of use in statistical problems concerning estimation and hypothesis testing. However, their use is much wider; these methods are used in antispam filters of electronic mail or in the game theory. Definitions, theo rems, proofs and examples are included in the paper for this purpose to enable easier understanding of particular topics. The paper is helpful mainly because of the fact that as yet there are not many books in Czech language dealing with Bayesian methods. 1


Tests of normality of time series
Stibůrek, David ; Anděl, Jiří (advisor) ; Kulich, Michal (referee)
This work considers testing normality of time series in AR and ARMA processes. Firstly we investigate properties of common normality tests, which assume independency. The main goal is to examine levels and powers of tests in dependence on distances of the roots of the characteristic polynom from unit circle. After this we study the tests, which don't assume independency. In the case of AR processes, we get good results by testing normality of residuals. More complex tests can also give good results, but these tests need many observations and are difficult from the numerical point of view.

 

Weighted Data Depth and Depth Based Discrimination
Vencálek, Ondřej ; Hlubinka, Daniel (advisor) ; Anděl, Jiří (referee) ; Malý, Marek (referee)
The concept of data depth provides a powerful nonparametric tool for multivariate data analysis. We propose a generalization of the wellknown halfspace depth called weighted data depth. The weighted data depth is not affine invariant in general, but it has some useful properties as possible nonconvex central areas. We further discuss application of data depth methodology to solve discrimination problem. Several classifiers based on data depth are reviewed and one new classifier is proposed. The new classifier is a modification of knearest neighbour classifier. Classifiers are compared in a short simulation study. Advantage gained from use of the weighted data depth for discrimination purposes is shown.

 