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The uniformly most powerful test. The uniformly most powerful unbiased test
Sečkárová, Vladimíra ; Juríček, Jozef (advisor) ; Jurečková, Jana (referee)
Nazov prace: Stejuomrrne ncjsilnejsi test. Stejnomerne nojsilnejsi nestranny test Autor: Vladimira Seckarova Katcdra: Katedra pravdepodobnosti a matematickej statistiky Veduci bakalarskoj prace: Mgr. .Jozef Juricek e-mail voduceho: jurijlam@artax.karlin.mff.cuni.cz Al>strakt: Tato prtica sa zaobera prol)letnatikou testovania hypotez. konkretne existenciou rovnonierne najsilnejsieho a rovnomerne najsilnej.sicho nestrauueho testu. Prva kapitola olisahuje zakladno pojiny testovania hypote/. V druhej ka- pitole jo zayodcny pojein rovnomerne najsilnejsieho testu ako i jeho odvodenie v roznyeh obeenych ]>ripadoch i pro pa.rametre normalneho roxdelenia. Trctia. ka- pitola sa zaobera rovnomerne najsilnejsini ncstrannyin testom a jeho odvodonim obocnc a aj ])re parn.met.ro normalneho ro/,delenia. KlYieove .slov;i: testovanie hypotez, najsilnejsi test, rovnomerne naj.silnejsi test, rovnomerne najsilnejsi nc.stranny test Title: Uniformly most powerful test. Uniformly most powerful unbiased test Author: Vladimira Seckarova Department: Department of Probability and Mathematical Statistics Supervisor: Mgr. .lozef .luricek Supervisor's e-mail address: jurijlam@artax.karlin.mff.cuni.cz Abstract: In this work we study problems of hypotheses testing, particularly exis- tence of the uniformly most powerful and the uniformly...
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Cross-entropy based combination of discrete probability distributions for distributed decision making
Sečkárová, Vladimíra ; Kárný, Miroslav (advisor)
Dissertation abstract Title: Cross-entropy based combination of discrete probability distributions for distributed de- cision making Author: Vladimíra Sečkárová Author's email: seckarov@karlin.mff.cuni.cz Department: Department of Probability and Mathematical Statistics Faculty of Mathematics and Physics, Charles University in Prague Supervisor: Ing. Miroslav Kárný, DrSc., The Institute of Information Theory and Automation of the Czech Academy of Sciences Supervisor's email: school@utia.cas.cz Abstract: In this work we propose a systematic way to combine discrete probability distributions based on decision making theory and theory of information, namely the cross-entropy (also known as the Kullback-Leibler (KL) divergence). The optimal combination is a probability mass function minimizing the conditional expected KL-divergence. The ex- pectation is taken with respect to a probability density function also minimizing the KL divergence under problem-reflecting constraints. Although the combination is derived for the case when sources provided probabilistic type of information on the common support, it can applied to other types of given information by proposed transformation and/or extension. The discussion regarding proposed combining and sequential processing of available data, duplicate data, influence...
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Cross-entropy based combination of discrete probability distributions for distributed decision making
Sečkárová, Vladimíra ; Kárný, Miroslav (advisor) ; Jurečková, Jana (referee) ; Janžura, Martin (referee)
Dissertation abstract Title: Cross-entropy based combination of discrete probability distributions for distributed de- cision making Author: Vladimíra Sečkárová Author's email: seckarov@karlin.mff.cuni.cz Department: Department of Probability and Mathematical Statistics Faculty of Mathematics and Physics, Charles University in Prague Supervisor: Ing. Miroslav Kárný, DrSc., The Institute of Information Theory and Automation of the Czech Academy of Sciences Supervisor's email: school@utia.cas.cz Abstract: In this work we propose a systematic way to combine discrete probability distributions based on decision making theory and theory of information, namely the cross-entropy (also known as the Kullback-Leibler (KL) divergence). The optimal combination is a probability mass function minimizing the conditional expected KL-divergence. The ex- pectation is taken with respect to a probability density function also minimizing the KL divergence under problem-reflecting constraints. Although the combination is derived for the case when sources provided probabilistic type of information on the common support, it can applied to other types of given information by proposed transformation and/or extension. The discussion regarding proposed combining and sequential processing of available data, duplicate data, influence...
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Cross-entropy based combination of discrete probability distributions for distributed decision making
Sečkárová, Vladimíra ; Kárný, Miroslav (advisor)
Dissertation abstract Title: Cross-entropy based combination of discrete probability distributions for distributed de- cision making Author: Vladimíra Sečkárová Author's email: seckarov@karlin.mff.cuni.cz Department: Department of Probability and Mathematical Statistics Faculty of Mathematics and Physics, Charles University in Prague Supervisor: Ing. Miroslav Kárný, DrSc., The Institute of Information Theory and Automation of the Czech Academy of Sciences Supervisor's email: school@utia.cas.cz Abstract: In this work we propose a systematic way to combine discrete probability distributions based on decision making theory and theory of information, namely the cross-entropy (also known as the Kullback-Leibler (KL) divergence). The optimal combination is a probability mass function minimizing the conditional expected KL-divergence. The ex- pectation is taken with respect to a probability density function also minimizing the KL divergence under problem-reflecting constraints. Although the combination is derived for the case when sources provided probabilistic type of information on the common support, it can applied to other types of given information by proposed transformation and/or extension. The discussion regarding proposed combining and sequential processing of available data, duplicate data, influence...
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Interval estimates for binomial proportion
Borovský, Marko ; Zvára, Karel (advisor) ; Sečkárová, Vladimíra (referee)
The subject of this thesis is the point estimate and interval estimates of the binomial proportion. Interval estimation of the probability of success in a binomial distribution is one of the most basic and crucial problems in statistical practice. The thesis is divided into three chapters. The first chapter is about maximum- likelihood estimation for a binomial proportion. Futhermore, we will describe several methods of the construction of confidence intervals. In the end, we will compare all intervals in term of the actual coverage probability and expected length. 1
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The uniformly most powerful test. The uniformly most powerful unbiased test
Sečkárová, Vladimíra ; Jurečková, Jana (referee) ; Juríček, Jozef (advisor)
Nazov prace: Stejuomrrne ncjsilnejsi test. Stejnomerne nojsilnejsi nestranny test Autor: Vladimira Seckarova Katcdra: Katedra pravdepodobnosti a matematickej statistiky Veduci bakalarskoj prace: Mgr. .Jozef Juricek e-mail voduceho: jurijlam@artax.karlin.mff.cuni.cz Al>strakt: Tato prtica sa zaobera prol)letnatikou testovania hypotez. konkretne existenciou rovnonierne najsilnejsieho a rovnomerne najsilnej.sicho nestrauueho testu. Prva kapitola olisahuje zakladno pojiny testovania hypote/. V druhej ka- pitole jo zayodcny pojein rovnomerne najsilnejsieho testu ako i jeho odvodenie v roznyeh obeenych ]>ripadoch i pro pa.rametre normalneho roxdelenia. Trctia. ka- pitola sa zaobera rovnomerne najsilnejsini ncstrannyin testom a jeho odvodonim obocnc a aj ])re parn.met.ro normalneho ro/,delenia. KlYieove .slov;i: testovanie hypotez, najsilnejsi test, rovnomerne naj.silnejsi test, rovnomerne najsilnejsi nc.stranny test Title: Uniformly most powerful test. Uniformly most powerful unbiased test Author: Vladimira Seckarova Department: Department of Probability and Mathematical Statistics Supervisor: Mgr. .lozef .luricek Supervisor's e-mail address: jurijlam@artax.karlin.mff.cuni.cz Abstract: In this work we study problems of hypotheses testing, particularly exis- tence of the uniformly most powerful and the uniformly...
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Supra-bayesovská kombinace pravděpodobnostních distribucí
Sečkárová, Vladimíra ; Komárek, Arnošt (referee) ; Kárný, Miroslav (advisor)
In this work we study problems of sharing of probabilistic information by using Supra-Bayesian approach. In 1st Chapter the methods and formulas used in the work are mentioned. 2nd Chapter contains the introduction to discussed topic. In 3rd Chapter the main method of sharing the probabilistic information, which is based on common domain, is derived. In 4th Chapter the types of given knowledge pieces are specified, which are then transformed into probabilistic terms and extended on the whole domain. In 5th Chapter the results from the previous chapters are assessed.
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On Linear Probabilistic Opinion Pooling Based on Kullback-Leibler Divergence
Sečkárová, Vladimíra
In this contribution we focus on the finite collection of sources, providing their opinions about a hidden (stochastic) phenomenon, that is not directly observable. The assumption on obtaining opinions yields a decision making process commonly referred to as opinion pooling. Due to the complexity of the space of possible decisions we consider the probability distributions over this set rather than single values, exploited before, e.g., in [2]. The final decision (result of pooling) is then a combination of probability distributions provided by sources.
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A note on weighted combination methods for probability estimation
Sečkárová, Vladimíra
To successfully learn from the information provided by avail- able information sources, the choice of automatic method combining them into one aggregate result plays an important role. To respect the reliability in the source’s performance each of them is assigned a weight, often subjectively influenced. To overcome this issue, we briefly describe the method based on Bayesian decision theory and elements of infor- mation theory. In particular we consider discrete-type information, rep- resented by probability mass functions (pmfs) and obtain an aggregate result, which has also form of pmf. This result of decision making pro- cess is found to be a weighted linear combination of available information. Besides the brief description of the novel method, the paper focuses on its comparison with other combination methods. Since we consider the available information and unknown aggregate as pmfs, we mainly focus on the case when the parameter of binomial distribution is of interest and the sources provide appropriate pmfs.
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Tools for Decision Making under Uncertainty
Sečkárová, Vladimíra
In this paper we focus on two often considered distinct aims, namely maximizing of an utility function (e.g. an investment profit) and getting a more reliable global description of considered situation based on observed data (e.g. the final outcome of databases merging). In both cases we face the problem, that the data are unreliable, since they contain uncertainty caused by their source (i.e. human being). If we are looking for the optimum of the former aim, a game theory reformulation of the decision making task brings a smoother way to reach it. If the latter aim is considered, a merging procedure (also called fusion) processing the data should help us. This paper describes four recently developed methods dealing with decision making under uncertainty in two considered directions and one tool used for comparison of the fusion algorithms.
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