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Studium negaussovských světelných křivek pomocí Karhunenova-Loveho rozvoje
Greškovič, Peter ; Pecháček, Tomáš (advisor) ; Mészáros, Attila (referee)
We present an innovative Bayesian method for estimation of statistical parameters of time series data. This method works by comparing coefficients of Karhunen-Lo\`{e}ve expansion of observed and synthetic data with known parameters. We show one new method for generating synthetic data with prescribed properties and we demonstrate on a numerical example how this method can be used for estimation of physically interesting features in power spectra calculated from observed light curves of some X-ray sources.
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Bayesian probability distribution over a class of autoregression models applied to financial time series
Škerlík, Peter ; Šindelář, Jan (advisor) ; Hlávka, Zdeněk (referee)
In the present bachelor thesis we study the selection of appropriate autoregression models to forecast financial time series. We use Bayesian inference in statistics, which will be further explained. Consequently there is also given theoretical background which explains how to apply Bayesian inference to selection of models. The major contribution of the work is considered to be the application of this theoretical background to financial time series in programming environment C++ and the results of this application. The development of the probability of each autoregression model is shown in graphs. The results for Laplace and normal probability distribution of white noise in autoregression models are compared. The aim of the work is to provide the reader with enough theoretical information and to give him an practical overview of the usage of Bayesian statistics in data prediction. Also results of the work can be helpful to understand the mentioned models and to select the suitable model in practice.
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Empirický bayesovský přístup v mikromodelech pro výpočet rizika rezerv
Fedorčáková, Claudia ; Zimmermann, Pavel (advisor) ; Bílková, Diana (referee)
The traditional reserve estimation by an insurance company is based on the aggregated data. However, new trend is to utilize all the information available and analyse each claim separately. This way the application of claims specific features, such as non-proportional reinsurance or policy limits, is possible. The aim of this thesis is to construct the reserving model based on the individual claims. Following the recent legislative changes, the reserve risk has been redefined from ultimate claim horizon to a one-year risk horizon. Hence, the next task is to setup simulation model to calculate one year horizon reserve risk by updating the estimates based on new observations collected over one year. This is a typical task for Bayesian approach, therefore the model components are estimated using the tools of Bayesian statistics.
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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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