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Generating random pattern-avoiding matrices
Kučera, Stanislav ; Jelínek, Vít (advisor) ; Šámal, Robert (referee)
Binary matrices not containing a smaller matrix as a submatrix have become an interesting topic recently. In my thesis, I introduce two new algorithms to test whether a big square binary matrix contains a smaller binary matrix together with a process using randomness, which approximates a uniformly random matrix not containing a given matrix. The reason to create such algorithms is to allow researchers test their conjectures on random matrices. Thus, my thesis also contains an effective cross- platform implementation of all mentioned algorithms. Powered by TCPDF (www.tcpdf.org)
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Analysis of number lotteries
Jedličková, Veronika ; Pawlas, Zbyněk (advisor) ; Lachout, Petr (referee)
This bachelor thesis focuses on most well-known lotteries on the Czech market, in particular Sportka and Loto. Thesis observes many aspects influencing progress of these games. Winnning prices and lottery participant's expectations are examined. Total sum of these winnings is influenced by the amount of money in jackpot. Therefore, jackpot sum modelling and period between wins is taken into account. Moreover, expected period between two jackpot hits, distribution of drawn numbers and probability of drawing the same winning sequence is examined.
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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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Usage of Markov chains in banking
Klímová, Hana ; Marada, Tomáš (advisor) ; Prášková, Zuzana (referee)
The aim of the thesis is to get acquainted with the theory of Markov chains and to show how it is used in banking for estimation of credit rating transitions. In the first part, an introduction to the theory of discrete-time and continuous-time Markov chain with discrete state space is provided. In the next part three estimating methods that are used to calculate credit rating transitions - namely cohort method, durability method and Aalen-Johansen estimator are described theoreticaly. In the last part these methods are applied to calculate the matrices of transition probabilities on the basis of real rating migrations. Next an empirical transition matrix is used to simulate set of rating progressions, which are then used for estimating the original matrix by all the above mentioned methods. Finally the distance between the original and estimated matrices is evaluated to show the differences between the methods.
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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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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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Models of Queueing Systems
Horký, Miroslav ; Dvořák, Jiří (referee) ; Šeda, Miloš (advisor)
The master’s thesis solves models of queueing systems, which use the property of Markov chains. The queueing system is a system, where the objects enter into this system in random moments and require the service. This thesis solves specifically such models of queueing systems, in which the intervals between the objects incomings and service time have exponential distribution. In the theoretical part of the master’s thesis I deal with the topics stochastic process, queueing theory, classification of models and description of the models having Markovian property. In the practical part I describe realization and function of the program, which solves simulation of chosen model M/M/m. At the end I compare results which were calculated in analytic way and by simulation of the model M/M/m.
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Cross-channel attribution modelling
Žárský, Jiří ; Šperková, Lucie (advisor) ; Vraná, Lenka (referee)
This bachelor thesis focuses on attribution in the context of online marketing and studies available evaluation models for the performance of advertising campaigns. This performance is measured on the basis of the campaigns' effectiveness in catching the attention of customers and generating revenue. Data containing information about users' interactions with real advertising campaigns were used for the analysis. Prior to solving the attribution problem, data from the AdForm platform were cleansed and transformed into the required structures. This process is automated by the ETL tool called Keboola. Afterwards, data are analyzed using various attribution modelling techniques such as simple heuristics, the Shapley Value or Markov chains. The thesis discusses the theoretical side, as well as the actual application of these models. In the last section, the results of individual models are interpreted, taking into account the campaign costs. The interpretation is performed in the Tableau visualization software, using metrics such as the return on advertisement spending. This thesis presents a critical assessment of attribution models based on predetermined criteria. A scheme of data transformations, which can be used for future analyses of advertisement campaigns, was also created as part of this work. The thesis further includes a chapter discussing issues potentially leading to inaccuracies in the models' results.
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