SubjectsSubjects(version: 866)
Course, academic year 2019/2020
Selected topics in spatial modeling - NMTP602
Title: Vybrané partie z prostorového modelování
Guaranteed by: Department of Probability and Mathematical Statistics (32-KPMS)
Faculty: Faculty of Mathematics and Physics
Actual: from 2019 to 2019
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: not taught
Language: Czech
Teaching methods: full-time
Guarantor: prof. RNDr. Viktor Beneš, DrSc.
doc. RNDr. Zbyněk Pawlas, Ph.D.
RNDr. Michaela Prokešová, Ph.D.
Class: Pravděp. a statistika, ekonometrie a fin. mat.
Classification: Mathematics > Probability and Statistics
Annotation -
Last update: T_KPMS (27.04.2016)
The course deals with selected advanced topis in spatial modeling that follow the courses on spatial modeling and spatial statistics from master study. The main topics include limit theorems for point processes and geometric models, statistical inference for random fields, non-stationary models and space-time point processes. For PhD students.
Aim of the course -
Last update: T_KPMS (06.05.2014)

The aim of the course is to present some advanced modern topics in spatial modeling, spatial statistics and stochastic geometry.

Literature - Czech
Last update: T_KPMS (06.05.2014)

A. E. Gelfand, P. Diggle, P. Guttorp, M. Fuentes (eds.): Handbook of Spatial Statistics, Chapman & Hall/CRC, Boca Raton, 2010.

W. S. Kendall, I. Molchanov (eds.): New Perspectives in Stochastic Geometry, Oxford University Press, 2010.

R. Schneider, W. Weil: Stochastic and Integral Geometry, Springer, Berlin, 2008.

E. Spodarev (ed.): Stochastic Geometry, Spatial Statistics and Random Fields - Asymptotic Methods, Lecture Notes in Mathematics 2068, Springer, Heidelberg, 2013.

Teaching methods -
Last update: T_KPMS (06.05.2014)


Syllabus -
Last update: T_KPMS (06.05.2014)

1. ergodicity and mixing for spatial point processes, limit theorems for point processes and particle processes in large domains, approximation by m-dependent random fields

2. asymptotics for Poisson processes, stabilization theory, chaos decomposition and Stein’s method

3. random fields with continuous parameter, more advanced models, statistical methods, simulation

4. statistical inference for inhomogeneous and space-time point processes

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