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Recursive linear models and conditional independence structures
Zouhar, Jan ; Studený, Milan (advisor) ; Hlubinka, Daniel (referee)
Linear recursive systems (LRS) describe linear relationships among continuous random variables (typically, normally distributed ones). Acyclic oriented graphs are used to provide a qualitative description of these relationships. In a different branch of statistics, graphs serve as a means to describe conditional independence (CI) structures in systems of random variables. One of the aims of the thesis is to show that within the class of regular Gaussian distributions, both approaches coincide: for a given acyclic oriented graph, the statistical model of LRS specified by the graph is equivalent to a class of Gaussian distributions with CI structures that accord with the same graph. Furthermore, we generalized some of the relations between a graph of LRS and its CI structure outside the scope of Gaussian distributions. Another focus of the thesis is the relation between the graph of a LRS and the covariances among its variables. We derived a relationship that is analogous to the method of path coefficients which was introduced in the 1920s by the American geneticist Sewall Wright.
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Study of the dependence structure in economic and financial data
Hlavandová, Radana ; Zichová, Jitka (advisor) ; Petrásek, Jakub (referee)
Title: Study of the dependence structure in economic and financial data Author: Radana Hlavandová Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Jitka Zichová, Dr., Department of Probability and Mathematical Statistics Abstract: The thesis focuses on the issue of graphical models as a possible \\method for determining relationships between different variables. The thesis provides a broad theoretical basis for two methods of testing data, the test of zero partial correlation coefficients and the test based on maximum likelihood estimate. The last mentioned approach is a test of a graphical model with a data set on the basis of deviance. The thesis describes the theory of conditional independence and Markov properties as the basis of both tests, which are illustrated by general examples and by an example with real financial data. Keywords: partial correlation coefficients, conditional independence graph, graphical models
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Study of the dependence structure in economic and financial data
Hlavandová, Radana ; Zichová, Jitka (advisor) ; Petrásek, Jakub (referee)
Title: Study of the dependence structure in economic and financial data Author: Radana Hlavandová Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Jitka Zichová, Dr., Department of Probability and Mathematical Statistics Abstract: The thesis focuses on the issue of graphical models as a possible \\method for determining relationships between different variables. The thesis provides a broad theoretical basis for two methods of testing data, the test of zero partial correlation coefficients and the test based on maximum likelihood estimate. The last mentioned approach is a test of a graphical model with a data set on the basis of deviance. The thesis describes the theory of conditional independence and Markov properties as the basis of both tests, which are illustrated by general examples and by an example with real financial data. Keywords: partial correlation coefficients, conditional independence graph, graphical models
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Recursive linear models and conditional independence structures
Zouhar, Jan ; Studený, Milan (advisor) ; Hlubinka, Daniel (referee)
Linear recursive systems (LRS) describe linear relationships among continuous random variables (typically, normally distributed ones). Acyclic oriented graphs are used to provide a qualitative description of these relationships. In a different branch of statistics, graphs serve as a means to describe conditional independence (CI) structures in systems of random variables. One of the aims of the thesis is to show that within the class of regular Gaussian distributions, both approaches coincide: for a given acyclic oriented graph, the statistical model of LRS specified by the graph is equivalent to a class of Gaussian distributions with CI structures that accord with the same graph. Furthermore, we generalized some of the relations between a graph of LRS and its CI structure outside the scope of Gaussian distributions. Another focus of the thesis is the relation between the graph of a LRS and the covariances among its variables. We derived a relationship that is analogous to the method of path coefficients which was introduced in the 1920s by the American geneticist Sewall Wright.
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On Weakness of Evidential Networks
Vejnarová, Jiřina
In evidence theory several counterparts of Bayesian networks based on different paradigms have been proposed. We will present, through simple examples, problems appearing in two kinds of these models caused either by the conditional independence concept (or its misinterpretation) or by the use of a conditioning rule. The latter kind of problems can be avoided if undirected models are used instead.
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Proceedings of 6th Workshop on Uncertainty Processing
Vejnarová, Jiřina
The Workshops on Uncertainty Processing have been organized every three years since 1988 and are aimed at fostering creative intellectual activities and exchange of ideas in an informal atmosphere. The Proceedings contain 27 contributions selected by the Programme Committee for presentation at this year's Workshop.
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