|
|
Dose-response curves
Hezoučký, Martin ; Hlávka, Zdeněk (advisor) ; Maciak, Matúš (referee)
Title: Dose-response curves Author: Martin Hezoučký Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Zdeněk Hlávka, Ph.D., Department of Probability and Mathematical Statistics Abstract: In this thesis, we deal with the process of research and development of new medical substances with a focus on statistical methods used to determine appropriate doses. For this purpose, we examine the dose-response relationship. First, we describe a typical procedure for the development of a new drug. Second, we focus in detail on the MCP-Mod method. Third, we propose a new method based on the theory of gradual change models. This approach tests whether the administration of the drug has a significant effect. If so, the dose with desired effect is estimated using an appropriate model. Specifically, we provide an esti- mate using linear, quadratic and Emax gradual change models. We also describe a construction of a confidence interval for the point of change and also for the dose with the desired effect. The advantage of the proposed method over the MCP-Mod is the determination of the confidence intervals. Finally, we apply the above mentioned methods to data from the U.S. Tox21 research program and compare the results based on several tested substances and clearly demonstrate the...
|
|
|
Gradual change model
Míchal, Petr ; Hlávka, Zdeněk (advisor) ; Pešta, Michal (referee)
The thesis aims at change-point estimation in gradual change models. Methods avail- able in literature are reviewed and modified for point-of-stabilisation (PoSt) context, present e.g. in drug continuous manufacturing. We describe in detail the estimation in the linear PoSt model and we extend the methods to quadratic and Emax model. We describe construction of confidence intervals for the change-point, discuss their interpre- tation and show how they can be used in practice. We also address the situation when the assumption of homoscedasticity is not fulfilled. Next, we run simulations to calculate the coverage of confidence intervals for the change-point in discussed models using asymp- totic results and bootstrap with different parameter combinations. We also inspect the simulated distribution of derived estimators with finite sample. In the last chapter, we discuss the situation when the model for the data is incorrectly specified and we calculate the coverage of confidence intervals using simulations. 1
|
|
|
Bivariate negative binomial distributions
Šír, David ; Hudecová, Šárka (advisor) ; Hlávka, Zdeněk (referee)
The thesis summarizes basic properties of the negative binomial distribution, including estimations of unknown parameters which are derived with the help of the method of moments and the maximum likelihood method. The main part of the thesis describes the bivariate negative binomial distribution. Basic properties of the studied distribution are derived. For instance marginal distribution, distribution of the sum of elements and conditional distribution are negative binomial. The unknown parameters are estimated using the methods of moments and maximum likelihood method. The consistency and asymptotic normality of these estimators are proved. The final sample behaviour of the estimators is investigated in a small simulation study. The described bivariate distribution is applied to real traffic accidents data set from the Czech Republic. 1
|
|
|
Comparison of Models for Probabilities in Football Betting
Kožnar, František ; Večeř, Jan (advisor) ; Hlávka, Zdeněk (referee)
The aim of the thesis is to compare different statistical models for football betting odds and determine the best performing once based on the historical performance of sport teams. There are at least two possible approaches for computing the odds, namely Poisson regression and methods based on statistical machine learning. The idea is that the historical performance of teams is a good predictor of the future performance. Thus we can take the past performances, say all matches in the full season of the Bundesliga (306 matches), and use these data for predicting the odds for the following season. The resulting odds should be compared with the actual results using the scoring rules, which will identify the best performing model. 1
|
|
|
Robust estimation of autocorrelation function
Lain, Michal ; Hudecová, Šárka (advisor) ; Hlávka, Zdeněk (referee)
The autocorrelation function is a basic tool for time series analysis. The clas- sical estimation is very sensitive to outliers and can lead to misleading results. This thesis deals with robust estimations of the autocorrelation function, which is more resistant to the outliers than the classical estimation. There are presen- ted following approaches: leaving out the outliers from the data, replacement the average with the median, data transformation, the estimation of another coeffici- ent, robust estimation of the partial autocorrelation function or linear regression. The thesis describes the applicability of the presented methods, their advantages and disadvantages and necessary assumptions. All the approaches are compared in simulation study and applied to real financial data. 1
|
|
|
Comparison of Models for Probabilities in Football Betting
Kožnar, František ; Večeř, Jan (advisor) ; Hlávka, Zdeněk (referee)
The aim of the thesis is to compare different statistical models for football betting odds and determine the best performing once based on the historical performance of sport teams. There are at least three possible approaches for computing the odds, namely logistic regression, Poisson regression and methods based on statistical machine learning. The idea is that the historical performance of teams is a good predictor of the future performance. Thus we can take the past performances, say all matches in the full season of the English Premier League (380 matches), and use these data for predicting the odds for the following season. The resulting odds should be compared with the actual results using the scoring rules, which will identify the best performing model.
|
|
|
Statistical machine learning with applications in music
Janásková, Eliška ; Večeř, Jan (advisor) ; Hlávka, Zdeněk (referee)
The aim of this thesis is to train a computer on Beatles' songs using the re- search project Magenta from the Google Brain Team to produce its own music, to derive backpropagation formulas for recurrent neural networks with LSTM cells used in the Magenta music composing model, to overview machine learning techniques and discuss its similarities with methods of mathematical statistics. In order to explore the qualities of the artificially composed music more thor- oughly, we restrict ourselves to monophonic melodies only. We train three deep learning models with three different configurations (Basic, Lookback, and At- tention) and compare generated results. Even though the artificially composed music is not as interesting as the original Beatles, it is quite likeable. According to our analysis based on musically informed metrics, artificial melodies differ from the original ones especially in lengths of notes and in pitch differences be- tween consecutive notes. The artificially composed melodies tend to use shorter notes and higher pitch differences. 1
|
|
|
Yield Curves
Korbel, Michal ; Hurt, Jan (advisor) ; Hlávka, Zdeněk (referee)
The master thesis is looking into the estimation of yield curve using two ap- proaches. The first one is searching for parametric model which is able to describe the behavior of yield curve well and estimate its parameters. The parametric mo- dels used in the thesis are derived from the class of models introduced by Nelson and Siegel. The second approach is nonparametric estimation of yield curves using spline smoothing and kernel smoothing. All used methods are then compared on real observed data and their suitability for various tasks and concrete available observations is considered. 1
|
|
|
Zero inflated Poisson model
Veselý, Martin ; Komárek, Arnošt (advisor) ; Hlávka, Zdeněk (referee)
This paper deals with the zero-inflated Poisson distribution. First the Poisson model is defined and generalized to a zero-inflated model. The basic properties of this generalized model are derived. After- wards the basics of the method of moments and the maximum likelihood method are described. Both of these are used to derive parameter estimates of such distribution. The feasibility of calculating the distribution of moment method estimates is analyzed. Then the asymptotic distribution of maximum likelihood estimates is derived and used to create confidence intervals. In the last chapter a numeric si- mulation of the derived asymptotic properties is performed. Special attention is paid to situations where regularity conditions are not met. 1
|
|
|
Boxplot for multivariate data
Brabenec, Tomáš ; Nagy, Stanislav (advisor) ; Hlávka, Zdeněk (referee)
We will introduce three methods of extension of the classical Tukey's Boxplot for multivariate data. These are the Rangefinder, the Relplot and the Bagplot. To implement the methods, we will need the notions like Mahalanobis distance, elliptically symmetric distributions and halfspace depth. A big part of the thesis is focused on the construction of the Relplot and the Bagplot. We will also discuss, how do these methods detect outliers and what are their advantages and disadvantages. This work contains many examples and illustrating images. 1
|
guest ::
