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Analysis of AVG signals
Musil, Václav ; Sekora, Jiří (referee) ; Rozman, Jiří (advisor)
The presented thesis discusses the basic analysis methods of arteriovelocitograms. The core of this work rests in classification of signals and contribution to possibilities of noninvasive diagnostic methods for evaluation patients with peripheral ischemic occlusive arterial disease. The classification employs multivariate statistical methods and principles of neural networks. The data processing works with an angiographic verified set of arteriovelocitogram dates. The digital subtraction angiography classified them into 3 separable classes in dependence on degree of vascular stenosis. Classification AVG signals are represented in the program by the 6 parameters that are measured on 3 different places on each patient’s leg. Evaluation of disease appeared to be a comprehensive approach at signals acquired from whole patient’s leg. The sensitivity of clustering method compared with angiography is between 82.75 % and 90.90 %, specificity between 80.66 % and 88.88 %. Using neural networks sensitivity is in range of 79.06 % and 96.87 %, specificity is in range of 73.07 % and 91.30 %.
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Scenario generation for multidimensional distributions
Olos, Marek ; Dupačová, Jitka (advisor) ; Kaňková, Vlasta (referee)
Some methods for generating scenarios from multidimensional distribution assume we are able to generate scenarios from the one-dimensional distribution. We dedicate chapter 3 to this problem. At the end of the chapter, we provide references for applicable algorithms. Chapter 4 is focused on selected methods for generating scenarios from multidimensional distributions. In chapter 4.3, we introduce an algorithm for generating scenarios, which do not use any assumption about the distribution, except the first four moments and correlations to be specified. A method of generating scenarios based on approximation of multivariate normal distribution by the binomial distribution is described in chapter 4.5. Dimension reduction technique using principal components is presented in chapter 4.4. The algorithm is presented under the assumption of normal distribution. In chapter 4.6, we introduce the basics of the copula theory and a method for generating scenarios by C-vine copula. In chapter 5, we implement selected methods for generating scenarios for the estimation of daily value at risk for selected indexes and we discuss the results. Powered by TCPDF (www.tcpdf.org)
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Principal components
Zavadilová, Anna ; Hlávka, Zdeněk (advisor) ; Nagy, Stanislav (referee)
This thesis presents principal components as a useful tool for data dimensio- nality reduction. In the first part, the basic terminology and theoretical properties of principal components are described and a biplot construction is derived there as well. Besides, heuristic methods for a choice of the optimum number of prin- cipal components are summarised there. Subsequently, asymptotical properties of sample eigenvalues of covariance and white Wishart matrices are described and cases of equality of some eigenvalues are distinguished at the same time. In the second part of the thesis, asymptotic distribution of the largest eigenva- lue of white Wishart matrices is described, completed with graphic illustrations. A test of the number of significant eigenvalues is suggested on the basis of this limiting distribution, and the connection of this test to the number of suitable principal components is presented. The final part of the thesis provides an over- view of advanced computational methods for the choice of an adequate number of principal components. The thesis is completed with graphical illustrations and a simulation study using Wolfram Mathematica and R.
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Scenario generation for multidimensional distributions
Olos, Marek ; Dupačová, Jitka (advisor) ; Kaňková, Vlasta (referee)
Some methods for generating scenarios from multidimensional distribution assume we are able to generate scenarios from the one-dimensional distribution. We dedicate chapter 3 to this problem. At the end of the chapter, we provide references for applicable algorithms. Chapter 4 is focused on selected methods for generating scenarios from multidimensional distributions. In chapter 4.3, we introduce an algorithm for generating scenarios, which do not use any assumption about the distribution, except the first four moments and correlations to be specified. A method of generating scenarios based on approximation of multivariate normal distribution by the binomial distribution is described in chapter 4.5. Dimension reduction technique using principal components is presented in chapter 4.4. The algorithm is presented under the assumption of normal distribution. In chapter 4.6, we introduce the basics of the copula theory and a method for generating scenarios by C-vine copula. In chapter 5, we implement selected methods for generating scenarios for the estimation of daily value at risk for selected indexes and we discuss the results. Powered by TCPDF (www.tcpdf.org)
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Analysis of AVG signals
Musil, Václav ; Sekora, Jiří (referee) ; Rozman, Jiří (advisor)
The presented thesis discusses the basic analysis methods of arteriovelocitograms. The core of this work rests in classification of signals and contribution to possibilities of noninvasive diagnostic methods for evaluation patients with peripheral ischemic occlusive arterial disease. The classification employs multivariate statistical methods and principles of neural networks. The data processing works with an angiographic verified set of arteriovelocitogram dates. The digital subtraction angiography classified them into 3 separable classes in dependence on degree of vascular stenosis. Classification AVG signals are represented in the program by the 6 parameters that are measured on 3 different places on each patient’s leg. Evaluation of disease appeared to be a comprehensive approach at signals acquired from whole patient’s leg. The sensitivity of clustering method compared with angiography is between 82.75 % and 90.90 %, specificity between 80.66 % and 88.88 %. Using neural networks sensitivity is in range of 79.06 % and 96.87 %, specificity is in range of 73.07 % and 91.30 %.
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