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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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Image interpretation value and its purpose in creation of scientific figures and infographics
Phung, Hyu Nghia ; Sigmund, Tomáš (advisor) ; Horný, Stanislav (referee)
Graphic figures and various types of infographics have become an essential part of the scientific papers, business presentations and study materials. Although, authors of these documents often lack the knowledge of basic rules and principles of graphic design and learn how to create figures by trial and error. Literature addressing the issues of effective verbal (presentation skills) and non-verbal (principles of scientific writing) is available and accessible. Though literature addressing the issues of scientific figure design and general visual design are very few, sometimes non existent, despite the fact that images, figures and various charts are one of the most effective mediums for information sharing. This lack of material knowledge is detrimental to the quality of works of managers, professors and researchers. This thesis attempts to fill in this gap and motivate readers to further development and research of the issue. The thesis addresses the issue of figures from its core, those being the basic principles of image perception and interpretation. Building on concepts of theorists like Peirce, Saussure and Eco the thesis will then define the meaning and purpose of "Image Interpretation Value". Selected principles of figure construction and interpretation will be introduced. These principles will then be further analyzed and applied on the level of business and scientific figures. Each chapter will include various graphic figures and practical examples to enhance further understanding of the issue. The primary purpose and goal of this thesis is to create an easy-to-follow set of instructions and suggestions on how to design effective and intelligible figures to be used in the fields of business communication, scientific research and academic teaching.
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