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Use of Markov decision processes for modelling of collective games
Zákutný, Roman ; Antoch, Jaromír (advisor) ; Koubková, Alena (referee)
In this thesis, a model based on the continuous-time Markov process is built and implemented and later applied on an one chosen collective game. An extensive analysis of available data is carried out to build a regression model to estimate parameters of the game model. An usableness of the game model is shown by a simulation process. Pros and cons are evaluated in a comparison analysis against the application of the discrete-time Markov chains, how it was described in my bachelor thesis [Roman Zákutný (2007)]. In conclusion are discussed possible extensions for other collective games.
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Statistické odhady a chvosty jejich rozdělení pravděpodobností
Veverková, Jana ; Jurečková, Jana (advisor) ; Antoch, Jaromír (referee)
Master Thesis Statistical estimators and their tail behavior provides description of two type of characteristics of robustness of estimators - tail behavior and break- down point. Description is made for translation equivariant estimators in general and also for some concrete type of estimators, sample mean, sample median, trimmed mean, Huber estimator and Hodges Lehmann estimator. Tail behavior of these estimator is illustrated for random sample coming from t-distribution with 1 to 5 degrees of freedom. Ilustration is based on simulations made in Mathematica. 1
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Statistical analysis of interval data
Troshkov, Kirill ; Antoch, Jaromír (advisor) ; Branda, Martin (referee)
Traditional statistical analysis starts with computing the basic statisti- cal characteristics such as the population mean E, population variance V , cova- riance and correlation. In computing these characteristics, it is usually assumed that the corresponding data values are known exactly. In real life there are many situations in which a more complete information can be achieved by describing a set of statistical units in terms of interval data. For example, daily tempera- tures registered as minimum and maximum values offer a more realistic view on the weather conditions variations with respect to the simple average values. In environmental analysis, we observe a pollution level x(t) in a lake at different mo- ments of time t, and we would like to estimate standard statistical characteristics such as mean, variance and correlation with other measurements. Another exam- ple can be given by financial series. The minimum and the maximum transaction prices recorded daily for a set of stocks represent a more relevant information for experts in order to evaluate the stocks tendency and volatility in the same day. We must therefore modify the existing statistical algorithms to process such interval data. In this work we will analyze algorithms and their modifications for computing various statistics under...
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Regression models in survival analysis and reliability
Novák, Petr ; Volf, Petr (advisor) ; Antoch, Jaromír (referee) ; Dohnal, Gejza (referee)
Regression models in survival analysis and reliability Doctoral thesis Petr Novák Charles University in Prague, Faculty of Mathematics and Physics Abstract: In present work we study methods for modeling the dependence of data from sur- vival and reliability setting on available explanatory variables. The first part of the work compares the properties of the Cox proportional hazards model, Aalen additive model and the Accelerated failure model for survival data. We present methods for testing goodness-of-fit based on counting processes and martingale theory, allowing to identify which model fits the data best. The second part focuses on modeling the lifetime of repairable systems. We study the means of incorporating the history of studied devices into the models, including the influence of corrective repairs and preventive maintenance actions. We demonstrate the introduced methods on real applications and study their properties in various situations on simulated data. 1
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Matrix Algebra in Statistics
Navrátil, František ; Kulich, Michal (advisor) ; Antoch, Jaromír (referee)
of the bachelor thesis Title: Matrix Algebra in Statistics Author: František Navrátil Department: Department of Probability and Mathematical Statistics Supervisor: Doc. Mgr. Michal Kulich Ph.D. Abstract: The thesis deals with the theory of matrix algrebra, which is applicable in probability and statistics. The aim of the thesis is to summarize it in a clear and understandable way, so that the student familiar with the basics of matrix theory can expand his knowledge and use it in further studies. Therefore, the thesis contains many definitions and proved theorems, and examples to help understanding the theory. Applications are mentioned. It also provides references for further reading. The thesis begins with a brief summary of basic definitions and results in matrix algebra, which are covered in the usual courses on linear algebra. Subsequent chapters are specific, inter alia, for probability and statistics - in particular, they focus on special types of matrices and their properties, important matrix decompositions, functions of matrices and matrix difierentiation. Keywords: matrix algebra, statistics, idempotent matrix, spectral decomposition, Kronecker product
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Analysis of Biosensoric Data
Timková, Jana ; Hlávka, Zdeněk (advisor) ; Antoch, Jaromír (referee)
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Stochastic modellinf of epidemics
Vencálek, Ondřej ; Antoch, Jaromír (advisor) ; Brabec, Marek (referee)
Nazev prace: Stochasticke modelovani epidemii Autor: Oridfej Venealek Katedra: Katedra pravdepodobnosti a matenmticke sta.t.i.stiky Vedouci diplomove prace: Prof. RNDr. .Jaromi'r Antoch. CSe. e-mail vedoucfho: Jaromir.Antoch'3mff.cuni.c-/ Abstrakt: Tato diplomova prace se zabyva modelovanmi prevalence chfipky v Ceske repnb- lice v letech 2001 az 2003. Vychazi z dat laskave ZHpujccnych Statnhn zdravotm'm ustavem. Z hlediska epiclemiologie jde o observaeni deskriptivuf studii: zabyva se rozdelenhn poctu riernocnych chfipko\ v prnbehu sledovaneho ubdobi v ceske populaci. Matematiekym podkla- dem pro modelovaih je nelinearni hierarehicky model. Funkem tvar zavislo.sti prevalence na case vyehazt z teorie rustovyeh kfivek. Klicova slova: prevalence, sledovane obdobi, riistove kfivky, hierarehicky model Title: Stochastic- Modelling of Rpidemy Autor: (Jndrej Vencalek Department: Department of Probability and Mathematical Statistics Supervisor: Prof. RNDr. Jaronn'r Antoch, CSc. Supervisor's e-mail address: Jaromir.Antochl'0.|inff.ei.mi.cz Abstract: This diploma tbesis deals with modelling of prevalence of influenza in the C/ech Republic in the period from 2001 till 2003. It is based on data which were khidly lent by Statin' zdravotni nstav. This work is observational descriptive study from the view of epidemiology:...
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Analysis of extreme values
Vyhlídka, Jan ; Hendrych, Radek (advisor) ; Antoch, Jaromír (referee)
The goal of this thesis is to introduce basic concepts of the extreme value theory. The first chapter describes two fundamentally different approaches - block maxima and peaks over threshold models. Furthermore, it presents generalized extreme value distribution and generalized Pareto distribution. Moreover, relevant theorems and characteristics that are tied to these probabilistic distributions are discussed. The second chapter is a survey of various methods of parameter estimation of discussed distributions. The last chapter shows a simple application of how extreme value theory can be applied in finance on selected shares listed on the Prague Stock Exchange.
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Statistical image analysis in quality control
Legát, David ; Antoch, Jaromír (advisor) ; Dohnal, Gejza (referee) ; Tunák, Maroš (referee)
Title: Statistical image analysis in quality control Author: David Legát Department: Department of probability and mathematical statistics Supervisor: Prof. RNDr. Jaromír Antoch, CSc. Abstract: Currently, necessity to handle unstructured data rises significantly. One important area of unstructured data manipulation is signal processing such as audio and video, for which there exist many procedures. This work deals with the statistical approach to image processing, in which the image is interpreted as a representative of a random field. It describes two problems: removing noise from an image which facilitates better interpretation of the image, and image classification, in which we try to identify and recognize objects displayed. Part of the work aimed at eliminating of noise deals primarily with the use of MCMC simulation methods. These procedures can be tested in software that is included. Part of the work dealing with the classification of the image describes various modifications of classification trees methods. An example of image processing, which is the identification of defects in woven fabrics, is presented at the end. 1
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