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Performance comparison of methods for design of experiments for analysis of tasks involving random variables
Martinásková, Magdalena ; Novák, Drahomír (referee) ; Vořechovský, Miroslav (advisor)
The thesis presents methods and criteria for creation and optimization of design of computer experiments. Using the core of a program Freet the optimized designs were created by combination of these methods and criteria. Then, the suitability of the designs for statistical analysis of the tasks vith input random variables was assessed by comparison of the obtained results of six selected functions and the exact (analytically obtained) solutions. Basic theory, definitions of the evaluated functions, description of the setting of optimization and the discussion of the obtained results, including recommendations related to identified weaknesses of certain designs, are presented. The thesis also contains a description of an application that was created to display the results.
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Statistical analysis of interval data
Troshkov, Kirill ; Antoch, Jaromír (advisor) ; Branda, Martin (referee)
Traditional statistical analysis starts with computing the basic statisti- cal characteristics such as the population mean E, population variance V , cova- riance and correlation. In computing these characteristics, it is usually assumed that the corresponding data values are known exactly. In real life there are many situations in which a more complete information can be achieved by describing a set of statistical units in terms of interval data. For example, daily tempera- tures registered as minimum and maximum values offer a more realistic view on the weather conditions variations with respect to the simple average values. In environmental analysis, we observe a pollution level x(t) in a lake at different mo- ments of time t, and we would like to estimate standard statistical characteristics such as mean, variance and correlation with other measurements. Another exam- ple can be given by financial series. The minimum and the maximum transaction prices recorded daily for a set of stocks represent a more relevant information for experts in order to evaluate the stocks tendency and volatility in the same day. We must therefore modify the existing statistical algorithms to process such interval data. In this work we will analyze algorithms and their modifications for computing various statistics under...
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Principal components analysis and its applications
Dubová, Mária ; Hendrych, Radek (advisor) ; Prášková, Zuzana (referee)
In the present thesis, we deal with the principal components analy- sis. In the first of this text, we study different aspects of principals components, for instance, their derivation for a multidimensional random vector from general distribution or their calculation based on a covariance or correlation matrix. It is also important to choose the proper number of principal components for reducing the dimensionality of data in order to preserve most of information. Theoretical knowledge are illustrated with several examples. In the second part of the thesis, we focus on the value at risk. This term is defined in the text also with seve- ral usual formulas to calculate it. Then, we deal with a practical application of this concept and the principal component analysis. Concretely, we analyse the portfolio of some different interest rates to obtain the value at risk in some cases. 1
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Rendering of Voxel-Based Scenes Using Real-Time Ray Tracing
Menšík, Jakub ; Milet, Tomáš (referee) ; Matýšek, Michal (advisor)
The aim of this work was to create a program to visualize voxel scenes in real time using ray tracing. It included the study of various methods of such a rendering with a focus on shadows. The solution was created using Unity engine and experimental packages Unity Jobs and Burst. The thesis presents multiple ray tracing passes and SVGF technique, that is used to turn a noisy input into full edge-preserving image. The final program is able to render hard shadows, soft shadows, and ambient occlusion at speed of fifty frames per second.
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Normalized Inter-class Variance (NICV)
Vaněk, Stanislav
The internet of things leads to a massive interest in security of embedded devices. Nowadays, power analysis poses extremely effective and successful types of attacks to break confidential cryptographic algorithms such as AES (Advanced Encryption Standard), RSA (Rivest Shamir Adleman) and cryptographic devices such as smart cards. This paper deals with the method of localization of interesting markers in power analysis called NICV (Normalized Inter-Class Variance). The aim of the paper is to describe this method and its implementation.
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The Method of Standard Costing on Example of Specific Company
Kovářová, Kateřina ; Knorová, Kateřina (advisor) ; Krupička, Josef (referee)
The subject of the bachelor thesis is the method of standard costing and analysis of variances, that are both necessary for management and controlling of costs. It provides managers with information about the difference between actual and required state. The first part describes the theory of this method, where standard and subsequent analysis of variances are examined. In the second part, the bachelor thesis deals with company, that is part of a multinational concern. This company manufactures and designs electronic components. The author examines how the company applies the mentioned method and further analyzes the variances. Based on the results of the previous part, the author suggest possible improvements of this method.
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Monte Carlo methods in finance
Veselý, Václav ; Hurt, Jan (advisor) ; Kopa, Miloš (referee)
Monte Carlo simulation methods are very universal tool, which is applicable in many different cases. Major part of this work is devoted to variance reduction techniques and other improvements of Monte Carlo estimate. Practical examples of financial derivative pricing will be shown. 1
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Monte Carlo simulation of Counterparty Credit Risk
Havelka, Robert ; Šopov, Boril (advisor) ; Skuhrovec, Jiří (referee)
The counterparty credit risk is particularly hard to simulate and this thesis is only the second work so far, which considers effective simulation of couterparty risk. There are two new approaches to stochastic modelling, which are useful with respect to ef- ficient simulation of counterparty risk. These are Path-Dependent Simulation (PDS) and Direct-Jump to Simulation date (DJS). It had been show that DJS is far more ef- fective, when it comes counterparty risk simulation of path-independent derivatives. We focus on a portfolio of interest rate swaps, which are effectively path-dependent. DJS approach yields estimates with much lower variance than PDS approach. But as expected, the DJS is also much more computationally intensive. The increase in computing time in majority of cases wipes out any gains in lower variance and PDS approach is shown to be more effective, when computing time is taken into account. We also show that in practice the convergence rate of Monte Carlo method signif- icantly underestimates the true reduction in variance, which can be achieved with increasing number of scenarios. JEL Classification C02, C15, C63, G01, G12, G32 Keywords Monte Carlo, CVA, Exposure, Variance Author's e-mail robberth.cz@gmail.com Supervisor's e-mail boril.sopov@gmail.com
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Application of Management Control System in a Company
Kutišová, Kristýna ; Pavlicová, Iveta (referee) ; Žižlavský, Ondřej (advisor)
This Master's thesis is focused on dealing with cost variances (deviations) and using of standard costing method. The main intent is to analyse current state and make an improvement proposal of focusing on variables in company which is producing server PCs. This thesis is divided into three parts, which are theroretical part, analytic part and proposal part. The theoretical part is focused on characteristics of controlling, costs, calculation methods, especially standard costing method and focusing on variances. In next two parts is made the analysis of current state and then are suggested some improvement proposals.
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Principal components analysis and its applications
Dubová, Mária ; Hendrych, Radek (advisor) ; Prášková, Zuzana (referee)
In the present thesis, we deal with the principal components analy- sis. In the first of this text, we study different aspects of principals components, for instance, their derivation for a multidimensional random vector from general distribution or their calculation based on a covariance or correlation matrix. It is also important to choose the proper number of principal components for reducing the dimensionality of data in order to preserve most of information. Theoretical knowledge are illustrated with several examples. In the second part of the thesis, we focus on the value at risk. This term is defined in the text also with seve- ral usual formulas to calculate it. Then, we deal with a practical application of this concept and the principal component analysis. Concretely, we analyse the portfolio of some different interest rates to obtain the value at risk in some cases. 1
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