SubjectsSubjects(version: 849)
Course, academic year 2019/2020
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Spatial Modelling - NMTP438
Title in English: Prostorové modelování
Guaranteed by: Department of Probability and Mathematical Statistics (32-KPMS)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018 to 2019
Semester: summer
E-Credits: 8
Hours per week, examination: summer s.:4/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: English, Czech
Teaching methods: full-time
Guarantor: doc. RNDr. Zbyněk Pawlas, Ph.D.
Class: M Mgr. PMSE
M Mgr. PMSE > Povinně volitelné
Classification: Mathematics > Probability and Statistics
Pre-requisite : NMSA405
Is pre-requisite for: NMTP541, NMST543
Annotation -
Last update: doc. RNDr. Zbyněk Pawlas, Ph.D. (15.09.2013)
Random fields and spatial models on lattices, Markov random fields. Random measures on locally compact metric spaces, moment measures, Palm distribution. Point processes, stationarity, characteristics, Poisson process and other models of stationary point processes. Finite point processes with density, Markov point processes, inhomogeneous point processes, marked point processes.
Aim of the course -
Last update: doc. RNDr. Zbyněk Pawlas, Ph.D. (15.09.2013)

Introduce students into the basic methods for modelling of spatial data.

Course completion requirements -
Last update: doc. RNDr. Zbyněk Pawlas, Ph.D. (22.02.2019)

The course is finalized by a credit from exercise class and by a final exam.

The credit from exercise class is necessary for taking part in the final exam.

Requirements for receiving the credit from exercise class: regular active attendance (presenting solutions to at least 3 problems).

Attempt to receive the credit from exercise class cannot be repeated.

Literature -
Last update: doc. RNDr. Zbyněk Pawlas, Ph.D. (15.09.2013)

Cressie N.A.C.: Statistics for Spatial Data. Wiley, 1993.

Illian J., Penttinen A., Stoyan H., Stoyan D.: Statistical Analysis and Modelling of Spatial Point Patterns, Wiley, 2008.

Moller J., Waagepetersen R.P.: Statistical Inference and Simulation for Spatial Point Processes, Chapman&Hall/CRC, 2003.

Rataj J.: Bodové procesy, Karolinum, 2006.

Schabenberger O., Gotway C.: Statistical Models for Spatial Data Analysis. Chapman&Hall/CRC, 2005.

Teaching methods -
Last update: T_KPMS (16.05.2013)

Lecture+exercises.

Requirements to the exam -
Last update: doc. RNDr. Zbyněk Pawlas, Ph.D. (14.02.2018)

The final exam is oral. All material covered during the course may be part of the exam.

Syllabus -
Last update: T_KPMS (24.04.2015)

1. spatial models on lattices, Markov random fields, Ising model, Gaussian models

2. random fields, variogram, autocovariance function

3. random measures, existence, weak and vague convergence

4. point processes, Poisson process and other examples, moment measures, Palm distribution

5. stationary point processes, Cox process, cluster processes, hard-core point processes

6. finite point processes with density, Markov point processes

7. nonhomogeneous point process, marked point processes, marking models

Entry requirements -
Last update: doc. RNDr. Zbyněk Pawlas, Ph.D. (18.05.2018)

Fundamentals of measure theory, probability theory and stochastic processes.

 
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