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Thurstonian and statistical models in sensometrics
Cichrová, Michaela ; Antoch, Jaromír (advisor) ; Pešta, Michal (referee)
In this bachelor thesis, we study statistical models in sensometrics based on com- parison of samples. Firstly, we focus on Thurstonian approach to the problem, then we look at five procedures that are commonly used in sensometrics: 2-AFC, 3-AFC, duo-trio, triangle test and A-not A. These procedures are used for determining whether a percep- tible difference between two stimuli exists. The first four can also be used to determine whether no perceptible difference between two stimuli exists. For that we need to intro- duce the concept of equivalence testing. Furthermore, we will derive for 2-AFC, 3-AFC, duo-trio and triangle test their psychometric functions. We will also briefly compare the procedures. 1
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Confidence intervals for ratios
Krett, Jakub ; Omelka, Marek (advisor) ; Antoch, Jaromír (referee)
This thesis is devoted to the derivation of various types of confidence intervals for ratios of mean values. The inspiration for this work is applying the acquired theoretical knowledge to the problem of waste sorting, such as estimating the weight of the unsor- ted waste components concerning the total weight of the mixture. Firstly, the confidence intervals based on the standard asymptotic inference are derived, such as the standard asymptotic confidence interval and the interval estimate derived using the logit trans- formation. Furthermore, the thesis introduces the bootstrap method, which leads to the derivation of the basic, percentile, and studentized bootstrap confidence interval. Finally, the end of the thesis explores the properties of these interval estimates using two simu- lation models. 1
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Sensometric discriminant testing - comparison of paired comparison test and ranking test
Švarcová, Karolína ; Antoch, Jaromír (advisor) ; Omelka, Marek (referee)
Sensometric tests are useful for deciding if there exists a perceivable sensory difference between two or more products. The tests can be divided into two main groups - first for determining the existence of a difference based on a known and specified sensory attribute, and second for determination when the variance in the sensory attribute is not known. In this thesis we deal with sensometric tests from the first group and describe the contrast in the statistical approach of a test method that evaluates two samples and a test method evaluating more samples at once. Particularly, within the paired comparison test the calculations are based on the binomial distribution, whereas for the ranking test, statistical methods working with the ranks of random samples are used. To illustrate the process of a sensometric test, we execute a paired comparison test, and we show how a good test method for a given problem is chosen.
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Big data - extraction of key information combining methods of mathematical statistics and machine learning
Masák, Tomáš ; Antoch, Jaromír (advisor)
This thesis is concerned with data analysis, especially with principal component analysis and its sparse modi cation (SPCA), which is NP-hard-to- solve. SPCA problem can be recast into the regression framework in which spar- sity is usually induced with ℓ1-penalty. In the thesis, we propose to use iteratively reweighted ℓ2-penalty instead of the aforementioned ℓ1-approach. We compare the resulting algorithm with several well-known approaches to SPCA using both simulation study and interesting practical example in which we analyze voting re- cords of the Parliament of the Czech Republic. We show experimentally that the proposed algorithm outperforms the other considered algorithms. We also prove convergence of both the proposed algorithm and the original regression-based approach to PCA. vi
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Generalized estimating equaitons
Sotáková, Martina ; Omelka, Marek (advisor) ; Antoch, Jaromír (referee)
In this thesis we are interested in generalized estimating equations (GEE). First, we introduce the term of generalized linear model, on which generalized estimating equations are based. Next we present the methos of pseudo maximum likelyhood and quasi-pseudo maximum likelyhood, from which we move on to the methods of generalized estimating equations. Finally, we perform simulation studies, which demonstrates the theoretical results presented in the thesis. 1
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Runs and Randomness
Zdeněk, Pavel ; Čoupek, Petr (advisor) ; Antoch, Jaromír (referee)
In this thesis probability distribution of five random variables related to success runs in a sequence of Bernoulli trials was found. The techinque of imbedding random sequences into Markov chains is used and improved compared to existing results. For every run a Markov chain was constructed, the definiton of imbedding was verified, a method for computation of its distribution was stated and examples of distribution were computed. 1
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Total Least Squares and Their Asymptotic Properties
Chuchel, Karel ; Pešta, Michal (advisor) ; Antoch, Jaromír (referee)
Tato práce se zabývá metodou úplně nejmenších čtverc·, která slouží pro odhad parametr· v lineárních modelech. V práci je uveden základní popis metody a její asymptotické vlastnosti. Je vysvětleno, jakým zp·sobem lze v konceptu metody využít neparametrický bootstrap pro hledání odhadu. Vlastnosti bootstrap od- had· jsou pak simulovány na pseudo náhodně vygenerovaných datech. Simulace jsou prováděny pro dvourozměrný parametr v r·zných nastaveních základního modelu. Jednotlivé bootstrap odhady jsou v rovině řazeny pomocí Mahalanobis a Tukey statistical depth function. Simulace potvrzují, že bootstrap odhad dává dostatečně dobré výsledky, aby se dal využít pro reálné situace.
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Profit Maximization of Car Manufacturers Facing EU CO2 Emission Penalties From 2021
Leamer, Anthony David ; Večeř, Jan (advisor) ; Antoch, Jaromír (referee)
Title: Profit maximization of car manufacturers facing EU CO2 emission penalties from 2021 Author: Anthony David Leamer Department: Department of Probability and Mathematical Statistics Supervisor: prof. RNDr. Jan Večeř, Ph.D., Department of Probability and Mathematical Statistics Abstract: This paper sheds light on the newly coming emissions penalization sys- tem imposed on passenger vehicles registered in the EU. We analyze the penalty based on how it influences profit of the car manufacturers. After optimizing the profit margins car manufacturers impose on different vehicles we discuss what this means for the consumer and the manufacturer. We seek to answer the ques- tion 'Who is going to pay the penalty?'. In the last chapter we analyze real data to see if the penalty will motivate manufacturers to produce more eco-friendly passenger cars. The data shows that the manufacturers will lose profit until the fleets' average emissions fall within the limits. The maximization apparatus developed in this paper is indeed standard - in the sense that there are no new theories developed - although the problem is new to the extent that it requires new creative use of specific parts of optimization theory. Moreover the decision of the EU to implement drastic measures to bring down, 'on road CO2 emissions', leads...
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Big data - extraction of key information combining methods of mathematical statistics and machine learning
Masák, Tomáš ; Antoch, Jaromír (advisor)
This thesis is concerned with data analysis, especially with principal component analysis and its sparse modi cation (SPCA), which is NP-hard-to- solve. SPCA problem can be recast into the regression framework in which spar- sity is usually induced with ℓ1-penalty. In the thesis, we propose to use iteratively reweighted ℓ2-penalty instead of the aforementioned ℓ1-approach. We compare the resulting algorithm with several well-known approaches to SPCA using both simulation study and interesting practical example in which we analyze voting re- cords of the Parliament of the Czech Republic. We show experimentally that the proposed algorithm outperforms the other considered algorithms. We also prove convergence of both the proposed algorithm and the original regression-based approach to PCA. vi
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Geometric approach to the estimation of scatter
Bodík, Juraj ; Nagy, Stanislav (advisor) ; Antoch, Jaromír (referee)
In this thesis we describe improved methods of estimating mean and scatter from multivariate data. As we know, the sample mean and the sample variance matrix are non-robust estimators, which means that even a small amount of measurement errors can seriously affect the resulting estimate. We can deal with that problem using MCD estimator (minimum covariance determinant), that finds a sample variance matrix only from a selection of data, specifically those with the smallest determinant of this matrix. This estimator can be also very helpful in outlier detection, which is used in many applications. Moreover, we will introduce the MVE estimator (minimum volume ellipsoid). We will discuss some of the properties and compare these two estimators.
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