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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.
Last update: Pawlas Zbyněk, doc. RNDr., Ph.D. (15.09.2013)
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Introduce students into the basic methods for modelling of spatial data. Last update: Pawlas Zbyněk, doc. RNDr., Ph.D. (15.09.2013)
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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.
Attempt to receive the credit from exercise class cannot be repeated. Last update: Pawlas Zbyněk, doc. RNDr., Ph.D. (22.02.2023)
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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. Last update: Pawlas Zbyněk, doc. RNDr., Ph.D. (15.09.2013)
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Lecture+exercises. Last update: Pawlas Zbyněk, doc. RNDr., Ph.D. (14.02.2022)
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The final exam is oral. The topics for the exam are published on the lecturer's webpage. Last update: Pawlas Zbyněk, doc. RNDr., Ph.D. (14.02.2022)
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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 Last update: T_KPMS (24.04.2015)
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Fundamentals of measure theory, probability theory and stochastic processes. Last update: Pawlas Zbyněk, doc. RNDr., Ph.D. (18.05.2018)
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