|
| |
|
|
Didactics of statistics
Kvaszová, Milena ; Zvára, Karel (advisor) ; Půlpán, Zdeněk (referee) ; Fabian, František (referee)
The thesis Didactics of statistics is devoted to the problem of understanding of the basic concepts of probability theory and statistics. I have conducted a research in which I studied the understanding of the basic statistical concepts such as average, randomness, chance, variability, and sample by college students. I also studied whether the students are able to work with statistical data, whether they can read values from a chart, identify, and interpret their arithmetic mean. I interpreted the data obtained from the research using the model of the French psychologist Jean Piaget, according to which it is possible to distinguish three stages in the development of a theory, which Piaget named INTRA, INTER and TRANS. My research indicates that students' ideas about the basic statistical concepts are often very different from the ideas of the teacher. There is also interference between the scientific concepts and the similarly sounding terms of the everyday language. It is important that the teacher is aware of these differences and explains them using appropriate examples.
|
|
| |
|
|
Regression trees
Masaila, Aleh ; Hanzák, Tomáš (advisor) ; Zvára, Karel (referee)
Title: Regression trees Author: Aleh Masaila Department: Department of Probability and Mathematical Statistics Supervisor: Mgr.Tomáš Hanzák Abstract: Although regression and classification trees are used for data analysis for several decades, they are still in the shadow of more traditional methods such as linear or logistic regression. This paper aims to describe a couple of the most famous regression trees and introduce a new direction in this area - a combination of regression trees and committee methods, so called the regression forests. There is a practical part of work where we try properties, strengths and weaknesses of the examined methods on real data sets. Keywords: regression tree, CART, MARS, regression forest 1
|
|
|
Hardy-Weinberg equlibrium
Vlčková, Katarína ; Zvára, Karel (advisor) ; Kulich, Michal (referee)
In this paper, we describe various tests used to determine deviations from the Hardy-Weinberg equilibrium. The tests described are: the exact test, the χ2 test with and without continuity correction, the conditional χ2 test with and without continuity correction and the likelihood ratio test. These tests explore the question whether a random sample has trinomic distribution with probabilities pAA = θ2 , pAa = 2θ(1 − θ), paa = (1 − θ)2 . In this work, we simulate data of sample size 100 and we estimate the probability of type I error and the power of the tests. In this case, we get the best results with conditional χ2 test. The estimate of the power of the likelihood ratio test and the χ2 test is one of the highest of all. On the other hand, these two test are anticonservative in some cases . 1
|
|
|
Regression models with alternatively distributed response
Kučera, Tomáš ; Komárek, Arnošt (advisor) ; Zvára, Karel (referee)
This thesis deals with regression models in the case of binary response variable. Linear and logistic regression models are defined for different types of predictors. Then the thesis uses the theory of maximum likelihood and applies it to the special case of logistic regression model. Both exact inference of model parameters and hypothesis testing with related interval inference are discussed. Suitable methods for numerical solving of selected methods are suggested. In the final part, the discussed methods are applied to real credit scoring data from the field of banking, using the statistical software R.
|
|
|
Estimation and goodness-of-fit criteria in logistic regression model
Ondrušková, Markéta ; Hanzák, Tomáš (advisor) ; Zvára, Karel (referee)
In this bachelor thesis we describe binary logistic regression model and estimation of model's parameters by maximum likelihood method. Then we propose algorithm for the least squares method. In the goodness-of-fit criteria part we define Lorenz curve, Gini coefficient, C-statistics, Kolmogorov-Smirnov statistics and coefficient of determination R2 . We derive their relation to different sample coefficients of correlation. We derive typical relation between Gini coeffi- cient, Kolmogorov-Smirnov statistics and newly also coefficient of determination R2 via model of normally distributed score of bad and good clients. These derived teoretical results are verified on three real data sets. Keywords: Binary logistic regression, maximum likelihood, ordinary least squa- res, Gini coefficient, coefficient of determination. 1
|
|
|
Regression quantiles
Rusnák, Peter ; Kalina, Jan (advisor) ; Zvára, Karel (referee)
Title: Regression Quantiles Author: Peter Rusnák Department: Department of Probabilty and Mathematical Statistics Supervisor: RNDr. Jan Kalina, Ph.D.,Institute of Computer Science, AS CR Abstract: Quantile regression is a statistical method for specifying dependencies among variables, which was introduced by Koenker a Bassett in 1978. Since that time it has gone through a big development, when its theoretical properties have been under study, and it also has found many practical applications for data processing in variety of fields.While ordinary least-squares regression describes the relationship between one or more covariates X and the conditional mean of a response variable Y given X = x, quantile regression describes the relationship between X and the conditional quantiles of variable Y given X = x. This work contains the theory necessary for understanding relationship between standard and quantile regression and enabling include so received estimates to bigger group of M-estimates. The computation of coefficients for particular covariates is made by using Frisch-Newton algorithm belonging to methods of linear programming. The so-called regression ranks are also obtained as a by-product of this algorithm and we discuss their computational aspects and usage for hypothesis testing.In the second part, we...
|
|
|
Modeling progression of HIV disease
Žohová, Ivana ; Kulich, Michal (advisor) ; Zvára, Karel (referee)
In the present work we study modeling of HIV disease progression via multistate Markov model. The difficulty in this approach is how to define HIV disease states. These are usually defined in terms of CD4+ T lymphocyte counts, but this marker is a subject to biological fluctuation and, in real life, measurement errors as well. Estimating the model on such a data will lead to intensity estimates depending on frequency of observations. That is why we usually smooth the data before fitting the Markov model. In this work we studied two different approaches - linear mixed-effects model and local polynomial kernel estimator. All modeling is performed on real data and also an illustrative simulation example is included. Another issue considered in this work is determination of sero-conversion time. The sero-conversion distribution is derived based on time of last negative observation, first positive observation and last performed measurement.
|
|
|
Test for normality in the linear model
Hamplová, Blanka ; Hlávka, Zdeněk (referee) ; Zvára, Karel (advisor)
This diploma thesis is concerned with the means of verifying the assumption that the random component of the dependent variable in a linear model is normally distributed. Within the realm of a simulation study we observed how the use of various types of residuals in place of the original vector of errors impacts the ability of ten tests of normality to adhere to their significance levels. Because the individual residuals depend on the matrix of the model, four specific matrices of frequently used models were considered. In addition, the impact of the choice of a model along with the type of residuals on the power against five different alternative distributions of individual tests was studied. It turns out that the behavior of the tests is governed more by the type of the residuals used than by the choice of the model. In particular, studentized residuals appear to be unsuitable, because with their use the tests do not adhere to the prescribed significance level.
|
guest ::
RSS feed.