Generalized random tessellations, their properties, simulation and applications
Zobecněné náhodné mozaiky, jejich vlastnosti, simulace a aplikace
diploma thesis (DEFENDED)
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Permanent link
http://hdl.handle.net/20.500.11956/105167Identifiers
Study Information System: 194587
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- Kvalifikační práce [9279]
Faculty / Institute
Faculty of Mathematics and Physics
Discipline
Probability, mathematical statistics and econometrics
Department
Department of Probability and Mathematical Statistics
Date of defense
5. 2. 2019
Publisher
Univerzita Karlova, Matematicko-fyzikální fakultaLanguage
English
Grade
Excellent
Keywords (Czech)
Gibbsova zobecněná mozaika, algoritmus přidání a odebrání, vlastnosti stochastických modelů
Keywords (English)
Gibbs generalized tessellation, incremental-decremental algorithm, properties of stochastic models
The past few years have seen advances in modelling of polycrystalline materi- als using parametric tessellation models from stochastic geometry. A promising class of tessellations, the Gibbs-type tessellation, allows the user to specify a great variety of properties through the energy function. This text focuses solely on tetrahedrizations, a three-dimensional tessellation composed of tetrahedra. The existing results for two-dimensional Delaunay triangulations are extended to the case of three-dimensional Laguerre tetrahedrization. We provide a proof of existence, a C++ implementation of the MCMC simulation and estimation of the models parameters through maximum pseudolikelihood. 1