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Clustering and regression analysis of micro panel data
Sobíšek, Lukáš ; Pecáková, Iva (advisor) ; Komárek, Arnošt (referee) ; Brabec, Marek (referee)
The main purpose of panel studies is to analyze changes in values of studied variables over time. In micro panel research, a large number of elements are periodically observed within the relatively short time period of just a few years. Moreover, the number of repeated measurements is small. This dissertation deals with contemporary approaches to the regression and the clustering analysis of micro panel data. One of the approaches to the micro panel analysis is to use multivariate statistical models originally designed for crosssectional data and modify them in order to take into account the within-subject correlation. The thesis summarizes available tools for the regression analysis of micro panel data. The known and currently used linear mixed effects models for a normally distributed dependent variable are recapitulated. Besides that, new approaches for analysis of a response variable with other than normal distribution are presented. These approaches include the generalized marginal linear model, the generalized linear mixed effects model and the Bayesian modelling approach. In addition to describing the aforementioned models, the paper also includes a brief overview of their implementation in the R software. The difficulty with the regression models adjusted for micro panel data is the ambiguity of their parameters estimation. This thesis proposes a way to improve the estimations through the cluster analysis. For this reason, the thesis also contains a description of methods of the cluster analysis of micro panel data. Because supply of the methods is limited, the main goal of this paper is to devise its own two-step approach for clustering micro panel data. In the first step, the panel data are transformed into a static form using a set of proposed characteristics of dynamics. These characteristics represent different features of time course of the observed variables. In the second step, the elements are clustered by conventional spatial clustering techniques (agglomerative clustering and the C-means partitioning). The clustering is based on a dissimilarity matrix of the values of clustering variables calculated in the first step. Another goal of this paper is to find out whether the suggested procedure leads to an improvement in quality of the regression models for this type of data. By means of a simulation study, the procedure drafted herein is compared to the procedure applied in the kml package of the R software, as well as to the clustering characteristics proposed by Urso (2004). The simulation study demonstrated better results of the proposed combination of clustering variables as compared to the other combinations currently used. A corresponding script written in the R-language represents another benefit of this paper. It is available on the attached CD and it can be used for analyses of readers own micro panel data.
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Use of Interest Rate Models for Interest Rate Risk Management in the Czech Financial Market Environment
Cíchová Králová, Dana ; Arlt, Josef (advisor) ; Cipra, Tomáš (referee) ; Witzany, Jiří (referee)
The main goal of this thesis is to suggest an appropriate approach to interest rate risk modeling in the Czech financial market environment in various situations. Three distinct periods are analyzed. These periods, which are the period before the global financial crisis, period during the financial crisis and in the aftermath of the global financial crisis and calming subsequent debt crisis in the eurozone, are characterized by different evaluation of liquidity and credit risk, different relationship between financial variables and market participants and different degree of market regulations. Within this goal, an application of the BGM model in the Czech financial market environment is crucial. Use of the BGM model for the purpose of predicting a dynamics of a yield curve is not very common. This is firstly due to the fact that primary use of this model is a valuation of interest rate derivatives while ensuring the absence of arbitrage and secondly its application is relatively difficult. Nevertheless, I apply the BGM model to obtain predictions of the probability distributions of interest rates in the Czech and eurozone market environment, because its complexity, direct modeling of a yield curve based on market rates and especially a possibility of parameter estimation based on current swaptions volatilities quotations may lead to a significant improvement of predictions. This improvement was also confirmed in this thesis. Use of swaptions volatilities market quotations is especially useful in the period of unprecedented mone- tary easing and increased number of central banks and other regulators interventions into financial markets that occur after the financial crisis, because it reflects current market expectations which also include future interventions. As a consequence of underdevelopment of the Czech financial market there are no market quotations of Czech koruna denominated swaptions volatilities. I suggest their approximations based on quotations of euro denominated swaptions volatilities and also using volatilities of koruna and euro forward rates. Use of this approach ensures that predictions of the Czech yield curve dynamics contain current market expectations. To my knowledge, any other author has not presented similar application of the BGM model in the Czech financial market environment. In this thesis I further predict a Czech and Euro area money market yield curve dynamics using the CIR and the GP models as representatives of various types of interest rates models to compare these predictions with BGM predictions. I suggest a comprehensive system of three criteria, based on comparison of predicti- ons with reality, to describe a predictive power of selected models and an appropria- teness of their use in the Czech market environment during different situations in the market. This analysis shows that predictions of the Czech money market yield curve dynamics based on the BGM model demonstrate high predictive power and the best 8 quality in comparison with other models. GP model also produces relatively good qua- lity predictions. Conversely, predictions based on the CIR model as a representative of short rate model family completely failed when describing reality. In a situation when the economy allows negative rates and there is simultaneously a significant likelihood of their implementation, I recommend to obtain predictions of Czech money market yield curve dynamics using GP model which allows existence of negative interest rates. This analysis also contains a statistical test for validating the predictive power of each model and information on other tests. Berkowitz test rejects a hypothesis of accurate predictions for each model. However, this fact is common in real data testing even when using relatively good model. This fact is especially caused by difficult fulfilment of test conditions in real world. To my knowledge, such an analysis of the predictive power of selected interest rate models moreover in the Czech financial market environment has not been published yet. The last goal of this thesis is to suggest an appropriate approach to obtaining pre- dictions of Czech government bonds risk premium dynamics. I define this risk premium as a difference between government bond yields and fixed rate of CZK IRS with the same length. I apply the GP model to describe the dynamics of this indicator of the Czech Republic credit risk. In order to obtain a time series of the risk premium which are necessary for estimation of GP model parameters I firstly estimate yield curves of Czech government bonds using Svensson model for each trading day since 2005. Resulting si- mulations of risk premium show that the GP model predicts the real development of risk premiums of all maturities relatively well. Hence, the proposed approach is suitable for modeling of Czech Republic credit risk based on the use of information extracted from financial markets. I have not registered proposed approach to risk premium modeling moreover in the Czech financial market environment in other publications.
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Diagnostics for Robust Regression: Linear Versus Nonlinear Model
Kalina, Jan
Robust statistical methods represent important tools for estimating parameters in linear as well as nonlinear econometric models. In contrary to the least squares, they do not suffer from vulnerability to the presence of outlying measurements in the data. Nevertheless, they need to be accompanied by diagnostic tools for verifying their assumptions. In this paper, we propose the asymptotic Goldfeld-Quandt test for the regression median. It allows to formulate a natural procedure for models with heteroscedastic disturbances, which is again based on the regression median. Further, we pay attention to nonlinear regression model. We focus on the nonlinear least weighted squares estimator, which is one of recently proposed robust estimators of parameters in a nonlinear regression. We study residuals of the estimator and use a numerical simulation to reveal that they can be severely heteroscedastic also for data generated from a model with homoscedastic disturbances. Thus, we give a warning that standard residuals of the robust nonlinear estimator may produce misleading results if used for the standard diagnostic tools
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Modelling, parameter estimation, optimisation and control of transport and reaction processes in bioreactors.
ŠTUMBAUER, Václav
With the significant potential of microalgae as a major biofuel source of the future, a considerable scientific attention is attracted towards the field of biotechnology and bioprocess engineering. Nevertheless the current photobioreactor (PBR) design methods are still too empirical. With this work I would like to promote the idea of designing a production system, such as a PBR, completely \emph{in silico}, thus allowing for the in silico optimization and optimal control determination. The thesis deals with the PBR modeling and simulation. It addresses two crucial issues in the current state-of-the-art PBR modeling. The first issue relevant to the deficiency of the currently available models - the incorrect or insufficient treatment of either the transport process modeling, the reaction modeling or the coupling between these two models. A correct treatment of both the transport and the reaction phenomena is proposed in the thesis - in the form of a unified modeling framework consisting of three interconnected parts - (i) the state system, (ii) the fluid-dynamic model and (iii) optimal control determination. The proposed model structure allows prediction of the PBR performance with respect to the modelled PBR size, geometry, operating conditions or a particular microalgae strain. The proposed unified modeling approach is applied to the case of the Couette-Taylor photobioreactor (CTBR) where it is used for the optimal control solution. The PBR represents a complex multiscale problem and especially in the case of the production scale systems, the associated computational costs are paramount. This is the second crucial issue addressed in the thesis. With respect to the computational complexity, the fluid dynamics simulation is the most costly part of the PBR simulation. To model the fluid flow with the classical CFD (Computational Fluid Dynamics) methods inside a production scale PBR leads to an enormous grid size. This usually requires a parallel implementation of the solver but in the parallelization of the classical methods lies another relevant issue - that of the amount of data the individual nodes must interchange with each other. The thesis addresses the performance relevant issues by proposing and evaluation alternative approaches to the fluid flow simulation. These approaches are more suitable to the parallel implementation than the classical methods because of their rather local character in comparison to the classical methods - namely the Lattice Boltzmann Method (LBM) for fluid flow, which is the primary focus of the thesis in this regard and alternatively also the discrete random walk based method (DRW). As the outcome of the thesis I have developed and validated a new Lagrangian general modeling approach to the transport and reaction processes in PBR - a framework based on the Lattice Boltzmann method (LBM) and the model of the Photosynthetic Factory (PSF) that models correctly the transport and reaction processes and their coupling. Further I have implemented a software prototype based on the proposed modeling approach and validated this prototype on the case of the Coutte-Taylor PBR. I have also demonstrated that the modeling approach has a significant potential from the computational costs point of view by implementing and validating the software prototype on the parallel architecture of CUDA (Compute Unified Device Architecture). The current parallel implementation is approximately 20 times faster than the unparallized one and decreases thus significantly the iteration cycle of the PBR design process.
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Arctic tundra dendrochronology
Lehejček, Jiří ; Svoboda, Miroslav (advisor) ; Monika, Monika (referee)
Historically unprecedented environmental change in the Arctic ecosystems is often given into the context of its past and possible future development. In the region where instrumental meteorological observations are scarce archives need to be investigated in order to address this issues. The comprehensive synthesis one of the archives: long-live circumpolar evergreen Juniperus communis L. shrub is presented here. 20 individuals from southwest Greenland were investigated at the cell anatomy level to understand the ecology of the species and unhide its potential for environmental and climate reconstructions. The findings are as follows:
i) Stop of exponential cross-sectional conduit-lumen widening with increasing age is in contrast with conduit-lumen nature of trees. This indicates that shrubs do not need to saturate their water and nutrient demands via traits of classical hydraulic conductivity law but rather developed different mechanisms. Extreme weather conditions result in prostrate growth form. However, different weather factors probably influence shrub growth differently: While snow and wind act mechanically (a), temperature influences the form of growth physiologically (b). a) So long as the young shrub stem has high resilience to bend back to an upright position after snow melt and so long as it can withstand the wind during the vegetation season it most likely grows upright and the conduit-lumens widen. b) Temperature, resp. freeze-thaw events are responsible for the shrubs preference of safety (finite size of conduit-lumens) over hydraulic efficiency, thus not allowing for more primary growth. All of these (and other) factors are apparently working together and the transition of vertical to more horizontal growth is gradual. As a consequence, the conduit-lumen sizes may not have to be further increased (due to ecophysiological restrictions possibly also must not) because water is no longer transported against gravity.
ii) Observed age/growth trend has to be taken into consideration for further employment of the wood anatomical parameter in paleoenvironmental studies. That is, shrub cell parameters can only be used for this purposes if correctly detrended. This allows for more accurate as well as longer reconstructions because youth trend was often neglected in reconstructions based on shrub annual-rings.
iii) The south-western Greenland Ice-Sheet (GrIS) melt rates reconstruction is presented for the whole 20th century. This part of GrIS is considered as the most active. According to the presented reconstruction current GrIS melt rates are not uncommon for the last century being comparable to first decades of 20th century. This finding is particularly important contribution to the debate on Atlantic meridional overturning circulation (AMOC). Too high fresh water inputs into the Northern Atlantic from GrIS melting may slow down or even stop the AMOC which would result in more continental climate in Europe. Presented results indicate that this threshold lies higher than observed current melt rates of GrIS.
Fascinating Juniperus comunnis species has shown to be able to address many ecological as well as environmental open questions and due to its longevity and abundant distribution has a great potential to become an important player in the Arctic research.
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New Methods for Increasing Efficiency and Speed of Functional Verification
Zachariášová, Marcela ; Dohnal, Jan (referee) ; Steininger, Andreas (referee) ; Kotásek, Zdeněk (advisor)
Při vývoji současných číslicových systémů, např. vestavěných systému a počítačového hardware, je nutné hledat postupy, jak zvýšit jejich spolehlivost. Jednou z možností je zvyšování efektivity a rychlosti verifikačních procesů, které se provádějí v raných fázích návrhu. V této dizertační práci se pozornost věnuje verifikačnímu přístupu s názvem funkční verifikace. Je identifikováno několik výzev a problému týkajících se efektivity a rychlosti funkční verifikace a ty jsou následně řešeny v cílech dizertační práce. První cíl se zaměřuje na redukci simulačního času v průběhu verifikace komplexních systémů. Důvodem je, že simulace inherentně paralelního hardwarového systému trvá velmi dlouho v porovnání s během v skutečném hardware. Je proto navrhnuta optimalizační technika, která umisťuje verifikovaný systém do FPGA akcelerátoru, zatím co část verifikačního prostředí stále běží v simulaci. Tímto přemístěním je možné výrazně zredukovat simulační režii. Druhý cíl se zabývá ručně připravovanými verifikačními prostředími, která představují výrazné omezení ve verifikační produktivitě. Tato režie však není nutná, protože většina verifikačních prostředí má velice podobnou strukturu, jelikož využívají komponenty standardních verifikačních metodik. Tyto komponenty se jen upravují s ohledem na verifikovaný systém. Proto druhá optimalizační technika analyzuje popis systému na vyšší úrovni abstrakce a automatizuje tvorbu verifikačních prostředí tím, že je automaticky generuje z tohoto vysoko-úrovňového popisu. Třetí cíl zkoumá, jak je možné docílit úplnost verifikace pomocí inteligentní automatizace. Úplnost verifikace se typicky měří pomocí různých metrik pokrytí a verifikace je ukončena, když je dosažena právě vysoká úroveň pokrytí. Proto je navržena třetí optimalizační technika, která řídí generování vstupů pro verifikovaný systém tak, aby tyto vstupy aktivovali současně co nejvíc bodů pokrytí a aby byla rychlost konvergence k maximálnímu pokrytí co nejvyšší. Jako hlavní optimalizační prostředek se používá genetický algoritmus, který je přizpůsoben pro funkční verifikaci a jeho parametry jsou vyladěny pro tuto doménu. Běží na pozadí verifikačního procesu, analyzuje dosažené pokrytí a na základě toho dynamicky upravuje omezující podmínky pro generátor vstupů. Tyto podmínky jsou reprezentovány pravděpodobnostmi, které určují výběr vhodných hodnot ze vstupní domény. Čtvrtý cíl diskutuje, zda je možné znovu použít vstupy z funkční verifikace pro účely regresního testování a optimalizovat je tak, aby byla rychlost testování co nejvyšší. Ve funkční verifikaci je totiž běžné, že vstupy jsou značně redundantní, jelikož jsou produkovány generátorem. Pro regresní testy ale tato redundance není potřebná a proto může být eliminována. Zároveň je ale nutné dbát na to, aby úroveň pokrytí dosáhnutá optimalizovanou sadou byla stejná, jako u té původní. Čtvrtá optimalizační technika toto reflektuje a opět používá genetický algoritmus jako optimalizační prostředek. Tentokrát ale není integrován do procesu verifikace, ale je použit až po její ukončení. Velmi rychle odstraňuje redundanci z původní sady vstupů a výsledná doba simulace je tak značně optimalizována.
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Digital circuits test optimization by multifunctional components
Stareček, Lukáš ; Gramatová, Elena (referee) ; Kubátová, Hana (referee) ; Kotásek, Zdeněk (advisor)
This thesis deals with the possibilities of digital circuit test optimization using multifunctional logic gates. The most important part of this thesis is the explanation of the optimization principle, which is also described by a formal mathematical apparatus. Based on this apparatus, the work presents several options. The optimization of testability analogous to inserting test points and simple methodology based on SCOAP is shown. The focus of work is a methodology created to optimize circuit tests. It was implemented in the form of software tools. Presented in this work are the results of using these tools to reduce the test vectors volume while maintaining fault coverage on various circuits, including circuits from the ISCAS 85 test set. Part of the work is devoted to the various principles and technology of creating multifunctional logic gates. Some selected gates of these technologies are subject to simulations of electronic properties in SPICE. Based on the principles of presented methodology and results of multifunctional gates simulations, analysis of various problems such as validity of the modified circuit test and the suitability of each multifunctional gate technology for the methodology was also made. The results of analysis and experiments confirm it is possible for the multifunctional logic gate to optimize circuit diagnostic properties in such a way that has achieved the required circuit test parameter modification with minimum impact on the quality and credibility of these tests.
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Measuring phonological awareness – blend phoneme test in the beginning of schooling: an comparison of classical test theory and item response theory
Gorčíková, M. ; Šafr, Jiří
The main purpose of this paper is to show dis/advantages of two approaches classical test theory (CTT) and item response theory (IRT) to assess the level of diagnostic tools for evaluating phonemic awareness among first-grade students using longitudinal survey of children during the first grade of primary school (25 schools in Prague and Central Bohemia, 439 pupils). Phonemic awareness (FA) was measured by the task blend phonemes into syllables and words. The advantage of IRT compared to CTT is primarily a concept of independence of the test items. The probability of a response is dependent on the level of latent ability and characteristics of items. So if we know the characteristic of items parameter (difficulty) it could be estimated from the pupil´s responses the level of language skill for diagnostics. The results showed the need for blend phoneme test modifications (in particular for the end of the first grade) so as to adequately measure the high growth of FA ability levels during the first grade.
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How to prevent the proliferation of Legionella pneumophylis in hot water in the hospital Czech Krumlov
TUREK, Jan
This diploma thesis deals with microbiological quality of hot water in a hospital in Cesky Krumlov as well as hot water piping condition with respect to Legionella. It also deals with arrangements for improving the quality of hot water in this hospital. The subject and target of this thesis are the findings of the mentioned parameters based on own observations, technical documentation and analysis of warm water performed by an accredited laboratory. The hospital in Cesky Krumlov, the construction of which began in 1909, was built in 1911 as the 'Nemocnice Císaře Františka Josefa I.' As the time went by, new buildings were built up. The hospital was renamed to 'Všeobecná veřejná nemocnice' in 1942. In the following years the hospital expanded until the current condition. Water quality and presence of Legionella is a world-wide issue, which we must fight against. The thesis is divided into two parts. First, theoretical part, which includes both general and specific knowledge about Legionella, its health risks, the environment in which it occurs, possibilities of eliminating, suitability of the material for hot water pipes, gained in professional literature and a part of the Czech legislation dealing with public health protection, the law 'No. 258/2004 Coll.' in actual version and quality of drinking water and hot water. In the second, empirical part, I focus on the situation of the hospital in Cesky Krumlov from 2009 till 2015, concerning newly built boiler room and the whole distribution system of hot water regarding Legionella. Particularly I focused on materials used for ecologisation of the gas boiler room and materials used for hot water pipes and actual state of water distribution in individual buildings of this health care facility. I mentioned the analysis of the water samples performed by an accredited laboratory with corresponding technical documentation, which concerns the water distribution system, provided by the medical facility. I used secondary data analysis to evaluate these documents. Regarding the results from 2009 to 2015 the microbiological quality of warm water doesn't meet the limits defined in the Attachment No. 3 of the above mentioned law Order 252/2004 Coll. Limit value for colony forming units of Legionella is set to maximum of 100 CFU. In most of the samples this limit was exceeded by series of units up to hundred thousands of units. The last results in 2015 prove improvement of the unfavorable situation. In that year the analysis was tested three times. First in February, where the CFU units were 'only' in hundreds, with the top value of 550 CFU in the Postacute Care ward. Second analysis was performed in June that same year. Results were acceptable. The highest value was 64 CFU. Last analysis in the hospital was performed in December. Increased concentration of Legionella was again in the Surgery building. There were established of 1400 colony forming units. There were 300 CFU in the Postacute Care ward and the limit value of 100 CFU was in the ward of Internal medicine. The answers to research questions 'How to prevent reproduction of Legionella peumophylis in the water distribution system of the hospital in Cesky Krumlov?' and 'How to ensure a sufficient amount of quality hot water in the medical facility?' are included at the end of the stated recommendations. A risk factor causing the fast reproduction of Legionella is the old water distribution system in most of the buildings and low water temperature of water leaving the boiler, which is 55°C. All mentioned results and evaluations are included in this thesis as well as attached pictures, which show the environment and situation within the Health Care Institutions.
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