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Statistical analysis of censored data
Jakubcová, Monika ; Kulich, Michal (referee) ; Klášterecký, Petr (advisor)
Nazov prace: Statist icka analy/n cenzorovauych dat Antor: Monika .Ja.kubcova Katedra : Katedra pravdo])odol)iiosli a matematickej statisliky Vediici bakalarskej prace: Mgr. Petr Kla.sterecky e-itin.il veduccho: kla.stor.(i ka.rlin.niff.cuni.cz Abstrakt: Predlozena praca. podava prehlad o niektorych xakladnycli nieto- dach stat.isl.ickeho spracovania cenzorovaiiych dat. V iivodiiej kapitole uve- dieme akyni sposubom ccnzoruviUK'1 po/orovanio vxnika a pupi.seme zakladne typy cen/orova.nia,. Dalej sa oboznaminio s t'liukeijiini, ktcjre eeiixorova.ne data, popisujii a, icli v/ajomnymi v/,ta,hini. Nasleihu,1 nvedieine ne])arame- trlcke inet6(ly odluuln tyeht.o hinkcit. Uvedene odliady neskor ])ouzijeine pri koiistrukcii inter\alov S])olahli\"os(.i a ]>ri testovani hy]»)to/,. V xaverecnej kapitoh1 pripajame priklad, na ktorom deiuonst rnjeinc niektore z popi'saiiyoh inetod a spoyob praee s ( eii/orovaiiyiiii dat.a.ini v pro^,ra,ine R.. Kfueove slova: renzorovanie, eonzoroiiaiie data, funkria. pre/itia, Kaplanov- Meierov otlliad. log-rank test Title: Statistical analysis of censored data Author: Monika. Jakubcova Department.: Department of Probability and Mathematical Statistics Supervisor: Mgr. Petr KhlstenK'ky Suj)ervisor's e-mail address: klasterTikarlin.infr.cmii.cz Abstract: The presented work gives an...
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Testing of composite hypotheses in regression models with small sample size
Simerská, Olga ; Hlávka, Zdeněk (referee) ; Kulich, Michal (advisor)
The thesis, through a simulation study, examines the behaviour of asymptotic tests for testing hypotheses that several coefficients in logistic models are zero. Likelihood ratio, Wald's, and Rao's tests are considered. The necessary theory is formulated to derive the form of the statistics of asymptotic tests for testing composite hypotheses in logistic regression. Based on the numerical treatment of simulated data, the levels of significance of these tests are investigated, with critical values of the chi-squared distribution. The powers of the tests are then compared, modified empirically so that all tests reject the null hypotesis at the 5% level. The main focus is on the dependence of these values on the sample size and parameter settings.
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Applications of Markov processes to modeling HIV disease progression
Žohová, Ivana ; Prášková, Zuzana (referee) ; Kulich, Michal (advisor)
Nazev prace: Aplikace Mnrkovovych procesu pfi modclovaiii prubehu cho- n.hy HIV Autor: I\aua Zohova Katcdra: Katcdra pravdepodobnosli a malematicke statistiky Vedouci bakalafske prace: Mgr. Michal Ivulich,Ph.D. o-mail vedonciho: kulich fikarlm.mff'.cnni.c/ Abstrakt: V pfedio/ene praci se zabyvame slochastickym modelovam'm priibellii choroby HIV. pfedevshu pak inkubacni doln' AIDS. Hlavni po/or- noyt jc vuiiuvana. inorldlovdni |)oniuc( hoino^eiiiiicli Markovovych proce.sit sc s])ojit.yni c;isein a kouernou iniioziiion stavu. V praci ncjprvc Ktuclujoiric nOklora .spojili'i ro'/drloni, a to pft'devsiin z hk'diska jcjich vliodnosl.i k ino- dolovani inkulmrnf doby AIDS. Dalsi' cast jc vonovana konstnikci Ma.rko- vuvych niodelu. Pnilioh fihoroliv HIV jc iicjprvr niixlrlovaii poinorf dvou Iconkrntnicli inodrlu a jjotc pomoci zdliccnoDrhc) modclu. V niodelcch JHOTI odvox.cna. rozdrlrni inkubariii duljy AIDS. Klicova slova: chornba HIV. inkiiliariii doba AIDS. lhmiu»t'iim' Markovuv l>ro('{'s. Markovuv Title: Ap])lications of Markov processes to modeling, HIV di.scas siun Author: Ivana Zohuva Department: Drpartnicnt of Probability and MaHicniatical Statistics Supervisor: Mgr. Michal Kulich, Ph.D. Supervisor's e-mail address: kuhch^karhn.nifF.riirii.c? Abstract: In tlu1 present work \vc study stochastic modeling of...
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Stochastic models for genetic analysis
Selementová, Martina ; Zichová, Jitka (referee) ; Kulich, Michal (advisor)
Nazev prace: Slochasticke niodcly pro geneliekou analyzu Autor: MartinaSelementova Katedra: Katedra pravdepodobnosti a matematicke statistiky Vedouci bakalafske prace: Mgr. Michal Kulich, PhD, e-mail vedouciho: kuliclX^karlin.mff.cuni.cz Abstrakt: V pfedlozene praci studujerne elementarni stochasticke melody pro modelovani genetickych populaci. Nejprve uvadime zakladni pojmy obecne gcnetiky pro snadnejsi oricntaci v textu. V naslcdujicich kapitolach se zabyvame dynamikou vyvoje populace a zakladnimi problemy vyberu v populaci. lllavnim tcmatem je nahodne kfizeni v populaci, ktcre dale aplikujeme na pohlavne va/ane geny, letraploidy. autosterilizacni geny a na pfi'pad dvou lokusu. Ve druhe casti se xabyvame problemy vybcru: zamC'fili jsme se pf-edevsim na vyber xalozeny na gcnolypu aplikovany na pohlavi a pohlavne vazane geny a dale na lamiliarni vyber a konkretnf pn'klad Rh faktoru. Klicova slova: nahodne kfizeni, vyber Title: Stochastic Models for Genetic Analysis Author: Martina Selementova Department: Department oi'Probability and Mathematical Statistics Supervisor: Mgr. Michal Kulich, PhD. Supervisor's e-mail adress: kulich(«)karlin.mff.cuni.cz Abstract: In the presented work we study elementary stochastic methods for modeling genetic populations. First we show some basic notion of general genetics for...
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Effect of covariate measurement error on estimates and tests in regression models
Otčenášová, Eliška ; Jurečková, Jana (referee) ; Kulich, Michal (advisor)
The thesis concerns with e ect of covariate measurement error on the least squares estimators and tests of importance of parameters in regression models. It refers to unsatis ed assumptions of linear model when using measurement error covariates and resulting e ect on estimates and tests in regression models. It focuses mainly on investigation of consistence of estimates of linear and quadratic coeficient in additive and multiplicative model with one covariate with homoscedastic and heteroscedastic measurement error. In the nal chapter teoretical results are grounded by simulation study.
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