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Procedures for statistical control of random processes
Lebeda, Matěj ; Antoch, Jaromír (advisor) ; Hušková, Marie (referee)
Procedures for statistical control of random processes are well known. What we miss, is the comparison of such procedures. In the beginning, we will introduce the linear regression model which will be our assumption throughout the whole thesis. Then we will explain three most common violations of the model whereas two of them will be studied closely. In practice, two fundamental approaches are employed: offline and online approach. The offline methods are performed ex-post. We will propose procedures leaning on the assumption of normality, but robust procedures as well. Online methods (so called sequential) are based on a different principle. The most common are Shewhart's and CUSUM method. Finally, the last fifth chapter will be dedicated to comparison of these methods. Our main interests are to detect as fast as possible but also not before the time of change. The approaches will be compared from these aspects. 1
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Bayesian classification and regression trees
Dvořák, Martin ; Antoch, Jaromír (advisor) ; Maciak, Matúš (referee)
The bachelor's thesis is devoted to classification and regression trees, their con- struction, and interpretation. In the first part, the reader gets acquainted with the structure of decision trees, basic definitions, and methodology. In the second part, more advanced and efficient methods for creating such trees using a Bayesian approach to the whole problem are presented. The last part of the work is focused on a practical task, where knowledge from this work is used. The entire text is accompanied by pictures, explanations, and derivations to make it easier for the reader to understand the whole problem in more depth. The thesis Bayesian classification and regression trees can serve all those interested who want to learn more about the issue of decision trees. 1
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Confidence intervals for two-parameter exponential distribution
Špinka, Karel ; Kulich, Michal (advisor) ; Antoch, Jaromír (referee)
Abstract. In this work, we examine both point and interval estimators of two-parameter exponential distribution. We determine whether point estimates are unbiased, consistent, or both, and derive exact distributions from which confidence intervals can be construc- ted. We also demonstrate another method of creating confidence sets whose volume is, given certain conditions, the smallest possible on a specific confidence level. 1
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ROC curve
Zatkalíková, Zuzana ; Lachout, Petr (advisor) ; Antoch, Jaromír (referee)
This bachelor's thesis firstly defines the basic terms and then describes the ROC curve. Thesis deals with meaning of the ROC curve, its properties and construction with a graphic representation. Subsequently, the expression of the ROC curve and its area for normal, exponential and uniform distribution is derived in the work, also with a graphical representation. Then, it is related to statistical testing. At the end, there are described the empirical expression of the ROC curve and its application to real data processed in the Python programming language. 1
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Combining sensometric and optometric tests and analyses
Králik, Roman ; Antoch, Jaromír (advisor) ; Pešta, Michal (referee)
In this research, we embarked on an in-depth exploration to discern the moderately damaged beer from its pristine counterparts by non-professional consumers in a controlled social setting. The approach adopted was underpinned by the application of rigorous sta- tistical testing methodologies, with an underlying potential for further refinement to yield enhanced insights. Crucially, the study identified that the outcomes could be skewed by phenomena such as taster fatigue and the saturation of ambient air with light-struck odours, thereby necessitating their consideration. It occurs even though tests were taken in spacious, well ventilated, room and each taster had enough, 3 meters at least, space around him. The research innovatively combines the optometric measurements of beer samples' absorption with the findings from structured tastings, enabling assumptions to be made about the absolute threshold of beer damage that a statistically significant number of tasters is able to reliably detect. For Pilsner Urquell, the threshold of percep- tible damage was delineated to be in excess of 0.067 absorption units (a.u.). For Excel- lent 11ř, the damage threshold was calculated to fall within the range of 46 to 67 thou- sandths of absorption units (a.u.). When we compared results divided by gender, we concluded...
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Propp-Wilson algorithm
Urx, Vojtěch ; Beneš, Viktor (advisor) ; Antoch, Jaromír (referee)
This thesis deals with the theory leading up to the Propp-Wilson Algorithm and the application of this algorithm on the Ising model. The goal is to sum- marize the relevant theory from the book H¨aggstr¨om (2002) and solve some problems it gives to the reader. These problems consist of, among others, parts of the proof of correctness for a specific version of the Propp-Wilson algorithm on the Ising model and the Implementation of this algorithm in Python. 1
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Model averaging
Trusina, Filip ; Hlávka, Zdeněk (advisor) ; Antoch, Jaromír (referee)
The thesis aims to describe the method of model averaging and the construction of confidence intervals for dose estimation within the method MCP-Mod that is used for modeling the dose-response relationship. We define the doses EDp and MED, which are estimated in practice. We describe the MCP-Mod method, including suitable mod- els and contrast tests. We present information criteria, the ability to determine model weights based on information criteria and discuss their behaviour for different models and a growing number of observations. We also introduce three possible ways of con- structing confidence intervals for estimates obtained using the model averaging method. We apply these constructs to the example of dose-response modeling in a simulation study. Lastly, we introduce two new models with two change-points for modeling the dose-response relationship. 1
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Multivariate goodness-of-fit tests
Kuc, Petr ; Hlávka, Zdeněk (advisor) ; Antoch, Jaromír (referee)
In this thesis we introduce, implement and compare several multivariate goodness-of-fit tests. First of all, we will focus on universal mul- tivariate tests that do not place any assumptions on parametric families of null distributions. Thereafter, we will be concerned with testing of multi- variate normality and, by using Monte Carlo simulations, we will compare power of five different tests of bivariate normality against several alternati- ves. Then we describe multivariate skew-normal distribution and propose a new test of multivariate skew-normality based on empirical moment genera- ting functions. In the final analysis, we compare its power with other tests of multivariate skew-normality. 1
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