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Statistická analýza souborů s malým rozsahem
Holčák, Lukáš ; Hübnerová, Zuzana (oponent) ; Karpíšek, Zdeněk (vedoucí práce)
Tato diplomová práce je zaměřena na analýzu malých výběru, kde není možné získat větší počet dat. To může být způsobeno zejména z důvodu časového nebo ekonomického. Kde výroba nemá prostředky na uskutečnění většího počtu měření či jim to nedovolí nedostatek finančních prostředků. Samozřejme analýza malých výběrů je značně nejistá, protože závěry jsou vždy zatíženy značnou mírou nejistoty.
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Statistical analysis of laser spectroscopy measurements
Slávik, Ľuboš ; Bednář, Josef (oponent) ; Hübnerová, Zuzana (vedoucí práce)
The goal of this bachelor's thesis is to briefly describe Laser-induced breakdown spectroscopy method for analysis of elemental composition of studied samples. Outcomes of LIBS analysis (emission spectra) are further proceeded with mathematical methods of regression analysis. The goal is to find relations between measured chemical elements. These two methods are used for analysing real data based problem, that is to find specific relation between presence of uranium and hydrozirconium in a studied sample uranium-hosted sandstone.
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Modelování tenisového zápasu pomocí Markovského řetězce
Walica, Roman ; Hübnerová, Zuzana (oponent) ; Hrabec, Pavel (vedoucí práce)
Tato práce se zabývá aplikací Markovových řetězců v tenisovém odvětví a jejich následnou úpravou na základě formulovaných hypotéz. První část práce popisuje zásady tenisové hry. Ve druhé části se věnujeme pojmům z oblasti statistiky. Tyto pojmy jsou primárně využívány k vytváření a následnému větvení Markovových řetězců. Výsledkem této práce je několik Markovových řetězců pro tenisový game rozdělených dle podání, či příjmu nebo podle druhu povrchu, na kterém se zápas odehrává. Dalšími zmíněnými řetězci jsou pak řetězce pro tiebreak, set a zápas. Na konci práce uvádíme vypočtenou predikci výsledku a doby trvání tenisového zápasu a jeho modelovaných částí.
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Statistical models for prediction of project duration
Oberta, Dušan ; Žák, Libor (oponent) ; Hübnerová, Zuzana (vedoucí práce)
The aim of this thesis is to introduce statistical models suitable for data analysis and apply them on real data related to time duration of projects based on characteristics of given projects. In the first chapter, linear regression models based on the least squares method are studied, including their properties and prediction intervals. The next chapter deals with the problematics of generalized linear models, which are based on the maximum likelihood estimation principle. Also basic properties of generalized linear models and asymptotic confidence intervals for expected values are described. In the next chapter, regression trees are introduced, with two methods of growing the trees, namely least squares and maximum likelihood estimation. Also basic principles of pruning the trees and confidence intervals for expected values were described. Derivation of maximum likelihood estimation for regression trees and confidence intervals are to a great extent own work of the author. The last described models are random forests, including their basic properties and confidence intervals for expected values. Throughout these chapters, methods for assessing model's quality, selection of optimal submodel and finding optimal values for tuning parameters were also described. At the end, the studied models and algorithms are implemented in Python and applied on real data.
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Properties of Cauchy Distribution and their Applications
Quaye, Samson ; Žák, Libor (oponent) ; Hübnerová, Zuzana (vedoucí práce)
The Cauchy distribution plays a major role in biology, mathematics, physics and many related disciplines. As a consequence, a parameter estimation methodology for data which is distributed according to a Cauchy distribution is of importance. Nevertheless, the Cauchy distribution is well known for causing difficulties with classical approaches to parameter estimation. This diploma thesis is concerned with the study of the properties of Cauchy distribution. Several robust estimators of its location parameter are presented. A simulation study programmed in Python allows us to compare the performance of these parameter estimates in Bi-Cauchy ROC curve estimation. Moreover, some theoretical properties of the Bi-Cauchy ROC curve are studied.
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Modification of Regression Function
Popoola, Seyi James ; Hübnerová, Zuzana (oponent) ; Žák, Libor (vedoucí práce)
The regression analysis is a modelling technique that establishes, mathematically, the relationship between entities of a particular subject. Although the modelling is done in such a way that one variable is seen as a subject of the other(s), regression does not imply causation. The modeling has assumptions such as linearity, normality, little or no multicollinearity, homoscedasticity as conditions for optimal relationship establishment. The simplest of the regression technique is the linear regression which also is the most commonly used. It involves the use of a straight line model to define the best pattern of relationship. This best pattern is assessed by the measure of goodness of fit which describes the amount of variation in the response variable explained by the stimuli (or stimulus). Change-point regression is a type of linear regression that takes into account a change in course of the movement of the relationship under study. This type of change in course is taken into account by modelling the regression in segments to account for the entire relationship observable in the data at hand. Several information criterions are used for detecting this change in course, the Schwartz Information Criterion (SIC), the Bayesian Information Criterion (BIC), amongst others. The detection method adopted for this work is the Modified Information Criterion (MIC) which tests a null hypothesis of no change point against an alternative that states presence of change-point. The data upon which this methodology is applied is the Italy COVID-19 data. The data was subjected to a linear regression and evaluated after which it was subjected to this change point test and the test shows the presence of a change in course. The sections which the test divides the data into were modelled individually and their regression lines were obtained. The two sections were plotted on a graph with their regression lines intercepting at the crest of the plot.
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Autonomní jednokanálový deinterleaving
Tomešová, Tereza ; Žák, Libor (oponent) ; Hübnerová, Zuzana (vedoucí práce)
Tato práce se zabývá autonomním jednokanálovým deinterleavingem. Autonomní jednokánálový deinterleaving je proces separace přijaté sekvence radiolokačních impulzů od více emiterů na sekvence od jednotlivých emiterů, který jep rováděn bez lidské pomoci. Metody využívané pro úlohu deinterleavingu lze rozdělit dle počtu parametrů používaných pro separaci a to na jednoparametrické a víceparametrické metody. Tato práce se zabývá metodami především víceparametrickými. Jako vhodné metody pro autonomní jednokanálový deinterleaving byly vybrány DBSCAN algoritmus a variační bayesovské metody. Vybrané metody byly upraveny pro úlohu deinterleavingu a implementovány v programovacím jazyce Python. Jejich účinnost byla ověřena na simulovaných datech a datech z reálného provozu.
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Time series dynamic factor analysis
Slávik, Ľuboš ; Michálek, Jaroslav (oponent) ; Hübnerová, Zuzana (vedoucí práce)
This thesis studies a novel approach to time series clustering based on a dynamic factor model. Dynamic factor model is a dimension reduction technique enhancing classical factor analysis by a requirement of an autocorrelation structure of the latent factors. Parameters of the model are estimated via EM algorithm employing Kalman filtering and smoothing and necessary restrictions are placed on the model, so the model becomes identifiable. After describing the theoretical concept of the approach, the dynamic factor model is applied to the real observed time series and the work discusses its behaviour and properties on one-month meteorological data of fire weather index at 108 fire stations located in British Columbia. The procedure of the model estimates a loadings matrix of the model with a corresponding small number of latent factors and a variance-covariance matrix of the modeled time series. The thesis applies k-means clustering to the resulted loadings matrix and provides a division of the stations into clusters based on the reduced dimensionality of the original data. With the estimated cluster means and the latent factors, it is possible to obtain particular mean trends for each cluster. Then, the achieved clusters are compared with the results obtained for the same set of stations but within a different month to assess the stability of the clustering. The work discusses the effect of varimax rotation on the loadings matrix as well. Moreover, the thesis suggests a method for detecting possible time series outliers based on the estimated variance-covariance matrix of the model and discusses the effect of outliers on the estimated model.
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Models with Touchard Distribution
Ibukun, Michael Abimbola ; Karpíšek, Zdeněk (oponent) ; Hübnerová, Zuzana (vedoucí práce)
In 2018, Raul Matsushita, Donald Pianto, Bernardo B. De Andrade, Andre Cançado & Sergio Da Silva published a paper titled ”Touchard distribution”, which presented a model that is a two-parameter extension of the Poisson distribution. This model has its normalizing constant related to the Touchard polynomials, hence the name of this model. This diploma thesis is concerned with the properties of the Touchard distribution for which delta is known. Two asymptotic tests based on two different statistics were carried out for comparison in a Touchard model with two independent samples, supported by simulations in R.
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Statistical analysis of laser spectroscopy measurements
Slávik, Ľuboš ; Bednář, Josef (oponent) ; Hübnerová, Zuzana (vedoucí práce)
The goal of this bachelor's thesis is to briefly describe Laser-induced breakdown spectroscopy method for analysis of elemental composition of studied samples. Outcomes of LIBS analysis (emission spectra) are further proceeded with mathematical methods of regression analysis. The goal is to find relations between measured chemical elements. These two methods are used for analysing real data based problem, that is to find specific relation between presence of uranium and hydrozirconium in a studied sample uranium-hosted sandstone.
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