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Weighted Data Depth and Depth Based Discrimination
Vencálek, Ondřej ; Hlubinka, Daniel (advisor) ; Anděl, Jiří (referee) ; Malý, Marek (referee)
The concept of data depth provides a powerful nonparametric tool for multivariate data analysis. We propose a generalization of the well-known halfspace depth called weighted data depth. The weighted data depth is not affine invariant in general, but it has some useful properties as possible nonconvex central areas. We further discuss application of data depth methodology to solve discrimination problem. Several classifiers based on data depth are reviewed and one new classifier is proposed. The new classifier is a modification of k-nearest- neighbour classifier. Classifiers are compared in a short simulation study. Advantage gained from use of the weighted data depth for discrimination purposes is shown.
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Stochastic modellinf of epidemics
Vencálek, Ondřej ; Antoch, Jaromír (advisor) ; Brabec, Marek (referee)
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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Weighted Data Depth and Depth Based Discrimination
Vencálek, Ondřej ; Hlubinka, Daniel (advisor) ; Anděl, Jiří (referee) ; Malý, Marek (referee)
The concept of data depth provides a powerful nonparametric tool for multivariate data analysis. We propose a generalization of the well-known halfspace depth called weighted data depth. The weighted data depth is not affine invariant in general, but it has some useful properties as possible nonconvex central areas. We further discuss application of data depth methodology to solve discrimination problem. Several classifiers based on data depth are reviewed and one new classifier is proposed. The new classifier is a modification of k-nearest- neighbour classifier. Classifiers are compared in a short simulation study. Advantage gained from use of the weighted data depth for discrimination purposes is shown.
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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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