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Stochastic modellinf of epidemics
Vencálek, Ondřej ; Brabec, Marek (referee) ; Antoch, Jaromír (advisor)
Nazev prace: Stochasticke modelovani epidemii Autor: Oridfej Venealek Katedra: Katedra pravdepodobnosti a matenmticke sta.t.i.stiky Vedouci diplomove prace: Prof. RNDr. .Jaromi'r Antoch. CSe. e-mail vedoucfho: Jaromir.Antoch'3mff.cuni.c-/ Abstrakt: Tato diplomova prace se zabyva modelovanmi prevalence chfipky v Ceske repnb- lice v letech 2001 az 2003. Vychazi z dat laskave ZHpujccnych Statnhn zdravotm'm ustavem. Z hlediska epiclemiologie jde o observaeni deskriptivuf studii: zabyva se rozdelenhn poctu riernocnych chfipko\ v prnbehu sledovaneho ubdobi v ceske populaci. Matematiekym podkla- dem pro modelovaih je nelinearni hierarehicky model. Funkem tvar zavislo.sti prevalence na case vyehazt z teorie rustovyeh kfivek. Klicova slova: prevalence, sledovane obdobi, riistove kfivky, hierarehicky model Title: Stochastic- Modelling of Rpidemy Autor: (Jndrej Vencalek Department: Department of Probability and Mathematical Statistics Supervisor: Prof. RNDr. Jaronn'r Antoch, CSc. Supervisor's e-mail address: Jaromir.Antochl'0.|inff.ei.mi.cz Abstract: This diploma tbesis deals with modelling of prevalence of influenza in the C/ech Republic in the period from 2001 till 2003. It is based on data which were khidly lent by Statin' zdravotni nstav. This work is observational descriptive study from the view of epidemiology:...
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Analysis of Biosensoric Data
Timková, Jana ; Antoch, Jaromír (referee) ; Hlávka, Zdeněk (advisor)
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Is the Sportka game just?
Dvořák, Marek ; Antoch, Jaromír (referee) ; Čerbáková, Jana (advisor)
Nazev prace: Je Sportka spravedliva? AnLor: Marek Dvorak Katedra: Katedra. pravdepodobnosti a matematicke stalistiky Vedouci bakalnfske prace: Mgr. Jaua Cerbakova (.'-mail vedoiirihu: ja[irii.-erb'Lkarlin.mfi'.cuiii.ez Abstrakt: V pfedlo/one prad se zabyvame sazkovon loterii Sportka provo- xovanou v Ceske rei>ublice akciovon spolecnosti SAZKA. V uvodu prace zdnraziiujeme vyznam Sportky na trim loterii v OR a in'inasiiiu1 zakladni inibrnuicc1 o jejim vzniku a vyvoji. Po sti/namc'iii s pravidly hry a jojich ^inena.nii i>oeitaine ])ravdej)odol)nost.i vytazeni ciscl v zavislosti ua jediiot- livych po/Jcieh. Nask'duje vypocot. pravdrpodobnosti vyher v jc'duotlivych pofadieh v zj'u'islosti na zmrnaeh v ])ra\'idleeh Sportky. Hlavni cast prace obsahuje /akladni tvrzeni z tecn'ie testii dobro shody, ktere uaslediie innozni testovat hypotezu o ])aranietrech ninltiuouiiekeho rozdek'ni na /aklade napo- xorova.nych cetnosti la/rnyrli eisel. V za\'eru pfinasinic altei'nativni pohlcd na spravedlivost HporLky, ktery vyrlia/i z konceiitu ceiiy sazenky. Klicova slova: eel.nost, pra\dep(Klobnosti vyhor, Sportka, s])ra\'(.idlivost Title: Is Sporlka lair? Author: Marc:k Dvof;ik Departmrut: Do]iart.iiitjnL of Probal)ilily and Mathematical Statistics Supervisor: Mgr. Jana Oerl>akova SupervLsor's e-mail address:...
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Estimators of variance function in nonparametric regression
Hyklová, Bronislava ; Antoch, Jaromír (referee) ; Hušková, Marie (advisor)
The thesis studies variance function estimation in nonparametric regression model. It focuses on local polynomial estimators particularly. Exact expressions of conditional variance function estimator bias and covariance are derived and important asymptotical aproximations of these characteristics are also provided. Further the EBBS method for bandwidth selection and Dette's homoscedasticity test are described. Results of Prague Klementinum data processing are presented at the end of the thesis.
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Cluster analysis of large data sets: new procedures based on the method k-means
Žambochová, Marta ; Řezanková, Hana (advisor) ; Húsek, Dušan (referee) ; Antoch, Jaromír (referee)
Abstract Cluster analysis has become one of the main tools used in extracting knowledge from data, which is known as data mining. In this area of data analysis, data of large dimensions are often processed, both in the number of objects and in the number of variables, which characterize the objects. Many methods for data clustering have been developed. One of the most widely used is a k-means method, which is suitable for clustering data sets containing large number of objects. It is based on finding the best clustering in relation to the initial distribution of objects into clusters and subsequent step-by-step redistribution of objects belonging to the clusters by the optimization function. The aim of this Ph.D. thesis was a comparison of selected variants of existing k-means methods, detailed characterization of their positive and negative characte- ristics, new alternatives of this method and experimental comparisons with existing approaches. These objectives were met. I focused on modifications of the k-means method for clustering of large number of objects in my work, specifically on the algorithms BIRCH k-means, filtering, k-means++ and two-phases. I watched the time complexity of algorithms, the effect of initialization distribution and outliers, the validity of the resulting clusters. Two real data files and some generated data sets were used. The common and different features of method, which are under investigation, are summarized at the end of the work. The main aim and benefit of the work is to devise my modifications, solving the bottlenecks of the basic procedure and of the existing variants, their programming and verification. Some modifications brought accelerate the processing. The application of the main ideas of algorithm k-means++ brought to other variants of k-means method better results of clustering. The most significant of the proposed changes is a modification of the filtering algorithm, which brings an entirely new feature of the algorithm, which is the detection of outliers. The accompanying CD is enclosed. It includes the source code of programs written in MATLAB development environment. Programs were created specifically for the purpose of this work and are intended for experimental use. The CD also contains the data files used for various experiments.
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