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Application of (geo)demographic methods in education
Šebestík, Libor ; Hulíková Tesárková, Klára (advisor) ; Fialová, Ludmila (referee)
Application of (geo)demographic methods in education Abstract This master's thesis presents the possibilities of application of demographic, geodemographic and statistical methods on data published by the educational sector. The methods of demographic analysis are represented by the usage of rates, the concept of multistate demography (Markov chains) and the application of life tables. The enrollment ratio at particular levels of education, the average length of schooling and the number of dropouts from school grades are evaluated by these procedures. Markov chains which are based on the probabilities of transition between grades are also examined in terms of their use for forecasting purposes. These methods analyze the situation at the preschool, primary and secondary levels and are used on data from the annual Statistical Yearbooks on Education. In the field of geodemography, the so called preferential model of migration flows is presented. This model examines how applicants for tertiary education prefer or reject the regions of the Czech Republic for their tertiary education studies. The last method is the binary logistic regression which analyzes the inequalities in access to tertiary education. Both preferential model and logistic regression are based on data files on the admission process at...
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Mixing cards and convergence of Markov chains
Drašnar, Jan ; Prokešová, Michaela (advisor) ; Beneš, Viktor (referee)
This thesis presents mixing of a deck of cards as a random walk on the group of permutations. Perfectly shuffled deck of cards is defined as uniform distribution on this group. For analysis of the distance between the uniform distribution and the current distribution of the Markov chain generated by the shuffling quite general methods are used that can be applied to many other problems - i.e. strong stacionary time, coupling and transformation to an inverse distribution. In the last chapter the riffle shuffle is studied and a rather well-known fact is proved that seven or eight shuffles should be enough to shuffle a deck of 52 cards.
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Markov chains and credit risk theory
Cvrčková, Květa ; Prokešová, Michaela (advisor) ; Lachout, Petr (referee)
Markov chains have been widely used to the credit risk measurement in the last years. Using these chains we can model movements and distribution of clients within rating grades. However, various types of markov chains could be used. The goal of the theses is to present these types together with their advan- tages and disadvantages. We focus our attention primarily on various parameter estimation methods and hypotheses testing about the parameters. The theses should help the reader with a decision, which model of a markov chain and which method of estimation should be used for him observed data. We focus our attention primarily on the following models: a discrete-time markov chain, a continuous-time markov chain (we estimate based on continuous- time observations even discrete-time observations), moreover we present an even- tuality of using semi-markov chains and semiparametric multiplicative hazard model applied on transition intensities. We illustrate the presented methods on simulation experiments and simu- lation studies in the concluding part. Keywords: credit risk, markov chain, estimates in markov chains, probability of default 1
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Statistical problems in Markov chains with applications in finance
Chudý, Marek ; Prokešová, Michaela (advisor) ; Pawlas, Zbyněk (referee)
Title: Statistical problems in Markov chains with applications in finance Author: Marek Chudý Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Michaela Prokešová, Ph.D. Abstract: In this work, we study estimation methods for estimating transition probabilities in Markov chains. We discuss two methods, the first one for com- plete data and the second one for aggregate data. In the second chapter, we will introduce the theory for both methods and show examples of tests of sev- eral hypothesis about transition probabilities. In the last chapter we apply both methods to real data comming from an insurance company. In the last chapter we also present the results of both methods and compare them with each other. Keywords: Markov chains, transition probabilities, maximum likelihood method, least squares method
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Statistical Problems in Markov Chains
Adamová, Markéta ; Prášková, Zuzana (advisor) ; Branda, Martin (referee)
In this thesis we study basic statistical methods in Markov chains. In the case of discrete time, this thesis is focused on estimation of transition probability matrix and some basic tests (test for a specified transition probability matrix, test for homogeneity, test for independence, test for the order of Markov chain). In the case of continuous time we will concentrate on Poisson process and birth and death process. Estimation of parameters of these processes and tests for processes with specified parameters are mentioned. Developed estimates and test statistics are applied to real data in the final chapter.
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Language Identification of Text Document
Cakl, Jan ; Pešán, Jan (referee) ; Szőke, Igor (advisor)
The thesis deals with a language identification of a text document. The final program includes three different implementation methods of language identification. The first method is based on a frequency statistics of N-gram. The second one represents Markov chains and the last one uses the simulated neural net for the identification purposes. The result is implemented in the Python language.
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Music Improvisation
Angelov, Michael ; Hradiš, Michal (referee) ; Fapšo, Michal (advisor)
The thesis deals with problems concerning algorithmic music compositon, especially the domain of musical improvisation. There is an opening presentation of some of existing tools and approaches that are commonly used in domain of computer music. Consenquently there is a proposal of a new system, using main principles of markov chains and prediction suffix trees (PST) with description of its implementation. The main task of developped application is to analyze an external MIDI recording that is proposed to the system by user and create a new and inovative musical material in MIDI format that would sound close to the original recording giving an impression of a computer improvised music to the listener.
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Fuzzy Markov chains and their use in risk management
Šindelková, Petra ; Vymazal, Tomáš (referee) ; Misák, Petr (advisor)
This thesis deals with the application of Markov chains for the production of concrete products. The theoretical part is focused on clarifying the concepts of risk management and describes the procedures for dealing with classical Markov chains. There are presented basics of fuzzy logic and finally there is explained the procedure using fuzzy logic in calculating of classical Markov chains in the subsection entitled Fuzzy Markov chains. The practical part describes production process, namely concrete pavements. On this production process is applied knowledge from the theoretical part and there is a comparison and evaluation of two methods of Marcov chains calculation (classic and fuzzy approach).
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