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Application of statitistics to the measurement of characteristics of planar objects
Šedivý, Ondřej ; Beneš, Viktor (referee) ; Saxl, Ivan (advisor)
Nazev prace: Aplikace gcometricke statistiky na mefeni charakteristik rovinnych objektu Autor: Ondfej Sedivy Katcdra: Katedra pravdcpodobnosli a matematicke statistiky Vcdouci bakalafske pracc: RNDr. Ivan Saxl, DrSc, c mail vedouciho: saxl@math.cas.cz Abstrakt: Ci'lem prace je podat strucny a co nejpristupneji napsany pfehled odhadu charakteristik rovinnych objektu z vyberu ponzenych geometrickyini prostfedky. Prvni dvc kapitoly jsou obecncjst'ho razu. Pojednavaji o rozdilech mczi klasickym a geometrickym vyberem z populace a naznafiujf n^ktere zakladni principy dale vyuiivane. Naslcduji ukazky pouziti geomelrickc statistiky k odhadum zakladnich charakteristik pro rovinne souboiy bodu, kfivek a ploch. Kratka zaverecna stat'je včnovana zpusobu zkoumani trojrozmernych objektO. V textu jsou take podrobne zpracovany historicke Buffonovy ulohy ojehle a ctverci. Klicuva slova: geometricka statistika, klasicky a gcomctricky vybeY, Buffonovy ulohy Title: Application of geometrical statistics for measuring characteristics of planar objects Author: Ondfej Sedivy Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Ivan Saxl, DrSc. Supervisor's e-mail address: saxl@math.cas.cz Abstract: The aim of this work is to offer a short and clearly written review of estimations of characteristics...
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Cox point process
Kocúrová, Barbora ; Lechnerová, Radka (referee) ; Beneš, Viktor (advisor)
Na/ev praee: Coxfiv bodovy Autor: Barbara Kocnrova Katedra (ust.av): KalodrM pravdepodolmosli a uiatematicke statisiiky Vedonci bakalafske praee: Prof. KNDr. Viktor Beries, DrSe. e-mail vedonciho: Vikl nr.Benesviinlf.cuiti.e/ Abstrakt: V paidiozcur pr;ici st.ndujoinr bodovo prfjcesy. XabyvAine sr siniulac:i a, fil- trovannii Coxova bodovrlio proccsu ri/onclio Gauniia Onistehi-UhlonbeekovytTi jiro- tics^in. K odhadu uahodiir int.cn/ity C'oxova. pi'occsn jsnio zvolili bayesovsky jn'isiup s vynxitiui melody Mai'kov C'liain KJoiit.c C'urlo a Metrupolis-Hastiiigsova algoritinu rox(Mii a /.anikii pro bodovc Tit.k1: Cox point process Author: Harbora Kocnrova Dcparlinont: Dcpartinctit of Probability and Mnthrmatioa.j Statistics Supervisor: Prof. RiNDr. Viktor Hours, DrSc. Supervisor's e-uiail address Viktor.Benesf'inff.eniLi.c^ Abstract: hi the present work the spatial point processes, particularly Cox point pro- cess driven by Ganiina-Ornstoiu Uhlenberk process is studied. We also discuss how to simulate this Cox process and the tittering problem. To obtain the efficient [ilrored value we consider a Bayesiaii inference with using Markov C'liain Moult; Carlo me- thods and Birth-death Metropolis-Hastings algorithm.
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Segment point processes
Honzl, Ondřej ; Beneš, Viktor (referee) ; Pawlas, Zbyněk (advisor)
Naz-ev prace: Bodove proeesy usecek Aut.or: Ondrej Ilonzl Katedra: Katedra. pravdepodobnosti a matematicke statist,iky Vodonci bakalafske praee: RNDr. Zbynek Pawlas, Ph.D. e-mail vedouciho: zbynek.pawlas'O'mfl'.cmn.cz Abstrakt: Prace obsahnje strucny uvod do teoric bodovych procesii na nplnem se- parabilnim lokalne koutpakt iiiiu metrickem prost.oru. Hamcove je ziuinen si>ccii'ilni I>fipad st,acionariiilio ])roc:csu kouipaktiiich ninozin. Dale sc jiran1 vice1 /aincfujo na, Poissonuv prort\ usccek sc /nainyni ro/dcMrnim typickrho /rnu. V roviniirin pfi])aclo pak ukazujc n'i/nr odliady dolkovr int.i'ii/ily I'oissonova jiroccsu usccck, kU're jsou drfinovany na /aklade udaju /iskanych v okuc poxorovani. Hlavnim zajinoin prace st1 stava porovnavani tcclito odhadu die jujich rozpt.ylu. Cilem to- hoto sroviiavani ina byi stanovoni niezc \vlikoHti okna, klcra. fika, dokud jc Icpsi pou/it slozitojsi odhad a odkdy je naopak ro/ninno pouzit odliad. jclioz vvpocot jo snazsi, ale kl.cry pft'ilpoklada., zc inatiie vice iniormaci u po/orovanein JJI'OCCHU. Klicova slova: I'oissonuv i>roces. hodovy proces usccek, odhad delkove intonzit.y Title: Segment point Autlior: Ondrej Ilonzl Deijartuient: DepartiiieiiL ol'Prol)a.l>ilit.y and Mathcinalical Statistics Supervisor: KNDr. Zbyuek Pawlas, Ph.I). Supervisor's (^niail address:...
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Spatial modelling
Voldán, Adam ; Pawlas, Zbyněk (referee) ; Beneš, Viktor (advisor)
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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