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Stochastic Loss Reserving Models
Košová, Nataša ; Justová, Iva (advisor) ; Cipra, Tomáš (referee)
In present thesis we study and describe a stochastic loss reserve model for individual insurers. Specifically, it is the model based on the three following features. Modelling of expected claims depends on unknown parameters which estimates need to be the most accurate. Aggregated occurred and paid losses for particular years are modelled by a collective risk model. The final reserve is estimated by Bayesian methodology that uses a prior information from a significant number of insurers. Part of the thesis is also an implementation of the program that calculates reserves by using our model and its testing on simulated data.
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Introduction to Bayesian Statistics
Chuchel, Karel ; Komárek, Arnošt (advisor) ; Hušková, Marie (referee)
The aim of this thesis is to cover the basics of Bayesian inference. Bayesian logic is to consider parameter as a random variable with specific prior distribution. Prior distrubution can be chosen from wide range of possibilities. In this thesis miscellaneous choices of prior distribution are discussed and are followed with many examples. The another part of thesis concerns with building Bayesian point and interval estimates. Everything is compared to classical approach towards statistics. Last section shows the application of previous topics on real data.
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Knowledge Data Discovery
Jirmásek, Tomáš ; Chmelař, Petr (referee) ; Jurka, Pavel (advisor)
This bachelor's thesis deals with knowledge discovery in databases and is focused on Bayesian classification. The main goal of this thesis was to implement one of the methods of data mining and to verify its functionality on chosen data set. The application is implemented in programming language Java. MySQL database was chosen as a data storage for data set prepared to extract patterns from it. Information needed to start data mining task are gained from input DMSL document. The results of data mining are also stored into output DMSL document. The DMSL language had to be extended because of implemented method, Bayesian classification.
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Comparison of the Bayesian and Frequentist Approach to the Statistics
Hakala, Michal ; Karel, Tomáš (advisor) ; Malá, Ivana (referee)
The Thesis deals with introduction to Bayesian statistics and comparing Bayesian approach with frequentist approach to statistics. Bayesian statistics is modern branch of statistics which provides an alternative comprehensive theory to the frequentist approach. Bayesian concepts provides solution for problems not being solvable by frequentist theory. In the thesis are compared definitions, concepts and quality of statistical inference. The main interest is focused on a point estimation, an interval estimation, a statistical hypothesis testing and finally a stochastic convergence. The contribution of the thesis is a brief compilation of the Bayesian theory and introducing new arguments and examples in the discussion between proponents of the Bayesian and frequentist approach to statistics.
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Všudypřítomné exponenciální zobrazení a edukační aspekty interdisciplinární fyziky
Gottvald, Aleš
We emphasize the concept of exponential family and elucidate its ubiquitous and unifying role for interdisciplinary physics. We outline some metamorphoses of the exponential family in Bayesian Inference, Statistical Thermodynamics, Quantum Physics, Fourier Spectroscopy, Analytical Combinatorics, Sufficient Statistics, Symmetries and Lie Groups, Complex Systems (spiral geometries, power laws, phyllotaxis). On a heuristic level, the exponential family elucidates analogies between many seemingly scattered concepts and constructions, thus representing a tool of remarkable educational value. On a deeper epistemic level, the exponential faimly points out to some important ideas behind information physics and interdisciplinary science in general, thus representing a vivid research concept
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