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Spatial modelling
Voldán, Adam ; Beneš, Viktor (advisor) ; Pawlas, Zbyněk (referee)
Na/,ev praoe: Prost.orovc modolovam Antor: Adam Voldan Katedra: Katodra pravdepodobnosti ;v matematicke stal.istiky Vodouci bakalafske pracc: Proi. RNDr. Viktor Benes DrSc. e-mail vedouciho: Viktor.Bones'ohnff. emii.cz Abstrakt: V pfedlozene praci je stndovan nahodnv bodovy procos, konkretne permanent procos. Podrobne je probrana tcoric nahodnych bodovych pro- ce.su danych husLotou vzhlodeiu k Pois.sonove procesn. Sainotny proces je si- nuilovan inctodou Markov chain Mont.o Carlo, poinoci Mrtropolis-Hastingso- va algoritinu pro pcvuy pocct boili'i. Tento al^oi'itiuub ju naprogramovau v jazyce Pascal a vystupy toholo tnodoln json flalc vyhodnocovany v prograinn R-Spatstat, st.udovaiKj bylo pfodcvsiiu prostorove roznn'wteni bodii poinoci indexn dispor/c Kh'coxra .slova: Mc:!ro])olis-Ha,sting,siiv algoritnin.s. Poissc^nnv bodovy procos. pcniument procea Title: Spatial modelling Avithor: Adam VokUin De]jartment: Department of Probability and Mathoniatica.l Statistics Supervisor: Prof. RNDr. Viktor Bonos DrSc. Supervisor's e-mail address: Viktor.Bene.s^Cnifr.euni.e/, Abstract: In the present work we study stochastic point processes, especi- ally the permanent process. We introduce the theory of the stochastic point processes given by the density with respect, to the Poisson process. The per- manent process is...
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Stereological analysis of ellipsoids
Hájek, Tadeáš ; Pawlas, Zbyněk (advisor) ; Beneš, Viktor (referee)
In this thesis local stereological estimators of parameters of ellipsoidal shaped particles in a plane and in a three dimensional space are investigated. The main attention is devoted to the local estimators of ellipsoid volume based on the knowledge of the section of the ellipsoid by a line, a plane or a plane which contains a fixed line. We investigate densities, mean values and variances of these estimators. In the end, for a special case of ellipsoid - spheroid, the accuracy of estimators is compared through the use of coefficient of error. Powered by TCPDF (www.tcpdf.org)
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Markov point processes
Starinská, Katarína ; Staňková Helisová, Kateřina (advisor) ; Pawlas, Zbyněk (referee)
Nazov prace: Markovske boclove procesy Autor: KaUuhia Starinska. Katcdra: Katedra, pravdepodobnosti a matematickej statistiky Veduci bakalarskcj pracc: Mgr. Katefina Helisova e-mail vedouci'ho: helisova9": karlin.inft.cimi.cz Abstrakt: Markovske bodove procesy su niodely bodovych procesov so vza- jomnym posobem'm bodov. Tioto inodoly HI'I konstmovano uva/ovani'in husto- l,y bodovehcj proccsu vzlil'a.doni k P(ji.sH(jnovriiui proccsn a pridani'ni urcitych podmienok zaisl'\ijucic;h markovsku vlastnost. Prva cast sa zaobera zaklad- nyini dcfinicianii tykajuciini sa bodovych proccsov, Poisonovyni procesoin a procesmi danyini liustotou. Druba cast obsalmjc markovske bodovc pro- cosy a v trrtoj casti sn siniuliicic markovskyt;h bodovych procesov metodou Markov Chain ATontc Carlo. Pnica je nkoncc^ia simnlaciou Stranssovho pro- ecsn. KlfcoN-a slova: Poissouov bodovy proccs. markovsky bodovy procca, Markov Chain Monte Carlo Title: Markov point processes Author: Katarina Stariiiska Department: Department of Probability and Mathematical Statistics Supervisor: Mgr. Katefina Helisova Supervisor's e-mail atldrc^.ss: heliso\w^karlin.mff.cuni.cz Abstract: Markov point processes a.ro models for1 ])oint {processes with inter- acting points. Such models are constructed by considering a density for a point, process with respect...
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Urn models with stochastic replacements
Kochaniková, Petra ; Pawlas, Zbyněk (advisor) ; Dvořák, Jiří (referee)
The thesis purpose is to discuss urn models where the probability of success at any trial depends upon the number of previous successes. Such a scheme allows us to estimate the number of HIV cases among intravenous drug users. The coef- ficients in known probability generating function will be derived for the number of new infectives generated in both homogenous and inhomogenous population. The expectations and variances of the number of new infectives are also derived for both cases. These derived values will be verified for some fixed number of infectives and susceptibles by simulations. In the end of this thesis the studied model will be applied on a practical example where the effect of vaccination will be studied. 1
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Third order moment characteristics for spatial point processes
Verchière, Didier ; Prokešová, Michaela (advisor) ; Pawlas, Zbyněk (referee)
Moment characteristics are widely used for the statistical analysis of spatial point processes. Standard summary statistics used for the analysis of point processes are of first and second order (intensity, K -function, pair-correlation function...). Nonetheless, none of these characteristics describes the distribution of a point pattern completely. Higher order characteristics such as third-order characteristics can give more information about the spatial interactions. Two such characteristics have already been studied: the z -function (Moller et. al. 98) and the T -function (Schladitz, Baddeley 2000). Key words: T -function, z -function , third order moment characteristics.
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Bivariate distributions
Bednárik, Vojtěch ; Pawlas, Zbyněk (advisor) ; Klebanov, Lev (referee)
The thesis deals with three selected constructions of bivariate distributions. The first approach is to use the Fréchet bounds, which determine restrictions on the distribution function and the correlation coefficient of bivariate distribution. The second construction is the Plackett distribution which is a class of distributions containing the Fréchet bounds and the member corresponding to independent random variables. The third construction is a trivariate reduction method that is used for a construction of bivariate gamma, exponen- tial and Poisson distribution. Only bivariate Dirichlet distribution has slightly different construction. For the last four mentioned distributions the following basic characteris- tics are derived: density function, marginal distributions, correlation coefficient and some conditional moments, in case of exponential and Dirichlet distribution even conditional distribution. 1
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Firm Valuation
Baran, Jaroslav ; Pawlas, Zbyněk (advisor) ; Hurt, Jan (referee)
Xazev prace: Ocenovani pndnikii Aulor: Jaroslav Ha ran Katedra (iistav): Katedra pravdepodobnost i a mateniat icke statisliky Vedouci bakalarske pra.ce: HNDr. Zbynek Pawlas. Ph.D. e-mail vedoucfho: pawlas'.^'karlin.mtf.cnni.c/, Abslrakt: C'ileni prace je seznamif c.tenafe sc zfddadnhni a nejpon/iVanejsimi nastroji pro ohodnoceni akcii akciovycli spolecnosti. Druha cast. pra.ce so zabyva nitr'todaini odvoxt'iii a odliadu pai'ainetru pou/itych v modnlccli ororiovani. Jsiiu pr(i/('iit,ovaiiy zakladnf niodcly otvnnvani jako in^lnda sourasnr hodnoly budouci'cli prijniii a rclalivtii Dci-fiuvani, ktcrr \wr v uvahu tr/ui ccny srovnatelnych firciti. N'a konci pnicc jc jirakticky pri'klad occnrni spulrrnusti Nukia. Prace ina ypis in- Ibriuativiii chara.kU'i' a, ji-.jnn cilnn uoni prusadil konkirl.ni morlcl. ale srznainit, ctcnafc sc '/iikladiiiini prinripy ixTfiovani a poukaxat na vyhucly a ncvyhody uvc- drnych inodcln. Investor se nakoiiec nefidi ponze ]>odle niodehi (K-in'iovani. ale /a- iijine poatoj i diky oritatiiini /drojiiin inlorniaci. jako jsou media, vyrorni zpravy spcileeiiostf. /.pravy analytiku. vylih'dky trim atd. Klirova slova: ocenovani. soneasna liodnota, rust, urokova infra Title: Irinu valuation Author: .laroslav I'ia.ran De]jarlment: Depa,rlinent ol Proba.bility and Ma.thcnia,! ical Staiistics...
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Stochastic models for neural spike trains
Vörösová, Estera ; Pawlas, Zbyněk (advisor) ; Beneš, Viktor (referee)
K modelovaniu prenášaní správ v nervovom systéme sa dajú využi' časové bodové procesy. Cie©om práce je popísa' vybrané typy bodových procesov, kon- krétne: Poissonov proces, proces obnovy a Coxov proces. "alej analyzujeme reálne dáta, testujeme vhodnos' jednotlivých pravdepodobnostných modelov. Najprv sa zoznámime s históriou skúmania nervových impulzov ako bodových procesov. V prvej kapitole sú zhrnuté neurofyziologické základy fungovania neurónov. V dru- hej časti pozornos' je venovaná popise vybraných bodových procesov a v poslednej kapitole vyberieme model a testujeme jeho vhodnos' na reálnych dátach. 1
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Cluster point processes in insurance mathematics
Veselá, Veronika ; Pawlas, Zbyněk (advisor) ; Dostál, Petr (referee)
Title: Cluster point processes in insurance mathematics Author: Veronika Veselá Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Zbyněk Pawlas, Ph.D. Abstract: In the present work we study point processes and their importance in insurance mathematics. With the help of cluster and marked point processes we can describe a model that considers times of claim occurence and times and hei- ghts of corresponding payments. We study two specific models which can be used to predict how much money is needed for claims which happened. The first model is chain ladder in the form of Mack's model. For this model we show chain ladder estimators of development factors, estimates of their variance and their proper- ties. We try to find one-step ahead prediction and multi-step ahead prediction, which we use for calculating prediction of reserves. We shortly review asymptotic properties of the estimators in Mack's model. The second model is the Poisson cluster model. Firstly we define this model and the variables entering the model. Then we devote attention to one-step ahead and multi-step ahead prediction. We also study prediction when some variables have specific distributions. Finally, we use both methods of prediction on simulated data and compare their average relative absolute errors....
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Random tessellations and their statistical analysis
Vook, Peter ; Pawlas, Zbyněk (advisor) ; Dvořák, Jiří (referee)
Statistical aspects of random mosaics have not been heretofore given enough attention. This thesis deals with the derivation of estimators and statistical tests in a three-dimensional Poisson-Voronoi mosaic model. The first chapter compiles elementary results in the fields of point processes, random closed sets and particle processes. These are used in a second chapter to deduce geometric properties of random mosaics. The third chapter introduces the statistical research itself, estimators and model tests. Horvitz- Thompson estimator is introduced in order to correct statistics calculated on a reduced sample. Own results are tried in a computer simulation and compared to existing research in the last chapter. Mainly, the quality of estimators and the power of proposed tests is observed. 1
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