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Comparison of logistic regression and decision trees
Raadová, Zuzana ; Voříšek, Jan (advisor) ; Komárek, Arnošt (referee)
In this thesis we describe a classification of the binary data. For discussing this problem we use two well-known methods - logistic regression and decision trees. These methods deal with the problem in different way, so our aim is to compare a successfulness of their predictions. At first a model of logistic regression is introduced and we show how to estimate its parameters using a method of maximum likelihood. Then we describe decision trees as one of the most popular classification tools. There are discussed older classic algorithms CART and C4.5 and also two new algorithms GUEST and CRUISE. The predictions of both of the methods are shown on a real data example.
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Distance-based testing
Solnický, Radek ; Omelka, Marek (advisor) ; Komárek, Arnošt (referee)
When analyzing ecological data, one considers traditional multivariate techniques to be unsuitable. The use of dissimilarity coefficients and distance matrices is a way, how to solve this problem. In this work we present some of these coefficients and distance-based tests: Mantel test, several versions of ANOSIM and MRPP tests and distance-based test for homogeneity of multivariate dispersions. We focus on relationships among these tests and illustrate the use with an example. We also discuss the difficulties of interpretation of the results of these tests.
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Survival function estimation
Chrenko, Jakub ; Hudecová, Šárka (advisor) ; Komárek, Arnošt (referee)
Nazev prace: Odhady funkcr pfeziti Autor: Jakub Chrenko Kalodra: Katcdra pravdepodobnosti a mateinaticke statistiky Vedouci ba.ka.la.fske pra.ce: Mgr. Sarka Dosla e-mail vedouciho: dosla'ii'karlin.mff.cimi.cz Abstrakt: V pfedlozene pnici so zabyvame funkci pfeziti a jejuni odharly. Popsany jsou jak paramrtrirke, tak i neparamelrickc' pf ist upv. V obou piipa- deeh je pfihledimto k pfi'padncuiu ccnzorovanf clat. NoiJaramotricke rriotody iifkladon /adno pozadavky ua rozdrloni dat, a proto jsou uuiverzalne po- uzitcliic. Z tcchlo nictod uvadi'nir Z(^jmciH^ Ka,pkui-M(ucruv odhad fiinkcc pfcziti, jchoz zakladni vlastnosti jsou popsany. Ziiu'iiena je l.ra analyza ta- bulck unirtnosti. Parauietricke piist.upy j)rcdpokl;idaji koiikrntui tvar tno- rciickclio rozdeleiii sludovniio nahodric voliriny. Z nojcast.eji pouzivanycii rozdclonf Tivadinic oxporinucialui, Woilnilluvo a logaritniicko iioriualni. V za- vc.i'u prac'c; jsou tyt.o inctody poT'Oviiauy a ilustrovauy ua koukretui'm da- tovom souboru a poinoci simulaci. Klfcova slova: Fuiikcc })feziti, hazard, Kaplan-Mcicruv odhad, rouzorovana dat.n Title: Estiiua.tioii oi' Survivalship Function Author: Jakub Chronko Department: Department of Probability and Mathematical statistics Supervisor: Mgr. Snrka Dosla Supervisor's e-mail address: doslaCO'karliii.iiifl.ciuii.cz...
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Classification based on longitudinal observations
Bandas, Lukáš ; Komárek, Arnošt (advisor) ; Kulich, Michal (referee)
The concern of this thesis is to discuss classification of different objects based on longitudinal observations. In the first instance the reader is introduced to a linear mixed-effects model which is useful for longitudinal data modeling. Description of discriminant analysis methods follows. These methods ares usually used for classification based on longitudinal observations. Individual methods are introduced in the theoretic aspect. Random effects approach is generalized to continuous time. Subsequently the methods and features of the linear mixed-effects model are applied to real data. Finally features of the methods are studied with help of simulations.
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Cluster analysis for functional data
Zemanová, Barbora ; Komárek, Arnošt (advisor) ; Hušková, Marie (referee)
In this work we deal with cluster analysis for functional data. Functional data contain a set of subjects that are characterized by repeated measurements of a variable. Based on these measurements we want to split the subjects into groups (clusters). The subjects in a single cluster should be similar and differ from subjects in the other clusters. The first approach we use is the reduction of data dimension followed by the clustering method K-means. The second approach is to use a finite mixture of normal linear mixed models. We estimate parameters of the model by maximum likelihood using the EM algorithm. Throughout the work we apply all described procedures to real meteorological data.
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Introduction to Linear Mixed Models
Šaroch, Vojtěch ; Kulich, Michal (advisor) ; Komárek, Arnošt (referee)
of the bachelor thesis Title: Introduction to Linear Mixed Models Author: Vojtěch Šaroch Department: Department of Probability and Mathematical Statistics, MFF UK Supervisor: doc. Mgr. Michal Kulich Ph.D. Abstract: The thesis describes general procedures of estimation and hypothesis testing for linear statistical models. The models compare groups of observation due to dependent variable. Analysis of variance and linar mixed models are commonly used in the major science like pharmacology, biochemistry, economy and others. The thesis is appropriate for general public, because no advanced knowledge of probability and statistics are required. Particular methods are introduced gently and contain some practical examples for easier understanding of theory. Keywords: Analysis of variance (ANOVA), fixed and random effect, linear mixed model 1
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Simpson's paradox
Balhar, Jan ; Komárek, Arnošt (advisor) ; Kulich, Michal (referee)
Title: Simpson's paradox Author: Jan Balhar Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Arnošt Komárek, Ph.D. Supervisor's e-mail address: arnost.komarek@mff.cuni.cz Abstract: In this work we deal with Simpson's paradox and its more general version, called association reversal. We present definitions of these terms and necessary and sufficient conditions for their occurrence. Due to this, we get to issue of measuring relationship between two characters in 2x2 contigency table, we specifically mention advantages of odds ratio. We also try to answer, what relationship between two characters is, in case of Simpson's paradox, the right one. When looking for answer, we find, that ordinary statistical methods are not sufficient. It is necessary to identify causal relationships between characters. Therefore we get to issue of causality definition. Finally, we present some examples of Simpson's paradox in practice. Keywords: Simpson's paradox, association reversal, confounding, causality.
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Parametric regression models in survival analysis
Otava, Martin ; Komárek, Arnošt (advisor) ; Ševčík, Jaroslav (referee)
Na'/cv prace: Paraniot.ricke regiesiri modely v analv'/e pfezitf Autor: Martin Otava Katedra (li.stav): Katedra pravdepoiiolmosti a niatcmatitke statistiky Vedouci bakalafske prace: Mgr. Amost Komarek, Ph.D. (j-inail vedonciho: komaiek( >karlin.mli.cuni.c /, Abst.rakl: \ pfcdlo/.ene. praci studujcme panunetricke re^resni modely v ana- lyze pre/.ili. Skrze pojem cen/orovani se se/namfme s podst.alou analy/.y pixv.iti a zavudrme si zakladnf pojiiiy ir/ivanr v souvislo^ti s ui. Uka'/niK1 si tvurbu vlicxlnc'lio rc^rcsni'lio inodcln a zpiiwoby odliadti paranictru s diua/,cni na inotixhi inaxiinalni vrrohodnosTi spolrriu"' s itcrarniini nu'l.odaini pro ... vyrt'seni. Vysvrtlnnr si vv'/nani iialiodiu'' chyliy inefriii. Die1 jcjilio roxdrlcni pak vyLvoriiuc nckolik ni/nycli pai'a.iiHit.i1itikycli niodrlu pro odhad li\i.s(oly etiyu do sclhani. Srovnanir inodcly s neparamctrirkym odliadnn, ktdiy nain poimizc ... i t . /da na.s model odpovi'da ri'aliTr. CV-lou [iraci bude provaxcT ihi- ,stra,ce na skiilcrnycli dal(irh slouxicf jako nkii/ka fuii^cjvani metody v pra.xi. KliVova slova: Analv/a prc/iti. iJarainrtrickr inodcly. Title: Accclcralfd iailurc t.inn1 models in survival analysis Ant hor: Mart in Otava Dqiart.nieiit.: Depart.mcnl of Proba.bilit.y a.nd Mat lunnatical St.atisl.ics Supervisor: Mgv. Arnost Komarck,...
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Bayesian and Maximum Likelihood Nonparametric Estimation in Monotone Aalen Model
Timková, Jana ; Volf, Petr (advisor) ; Kraus, David (referee) ; Komárek, Arnošt (referee)
This work is devoted to seeking methods for analysis of survival data with the Aalen model under special circumstances. We supposed, that all regression functions and all covariates of the observed individuals were nonnegative and we named this class of models monotone Aalen models. To find estimators of the unknown regres- sion functions we considered three maximum likelihood based approaches, namely the nonparametric maximum likelihood method, the Bayesian analysis using Beta processes as the priors for the unknown cumulative regression functions and the Bayesian analysis using a correlated prior approach, where the regression functions were supposed to be jump processes with a martingale structure.
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