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.
Last update: doc. RNDr. Zbyněk Pawlas, Ph.D. (15.09.2013)
Náhodná pole a prostorové modely na mřížích, markovská náhodná pole. Náhodné míry na lokálně kompaktních metrických prostorech, momentové míry, Palmovo rozdělení. Bodové procesy, stacionarita, charakteristiky, Poissonův proces a další modely stacionárních bodových procesů. Konečné bodové procesy s hustotou, markovské bodové procesy, nehomogenní bodové procesy, kótované bodové procesy.
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.
Last update: doc. RNDr. Zbyněk Pawlas, Ph.D. (15.09.2013)
Seznámit studenty se základními možnostmi modelování prostorových dat.
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.
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: doc. RNDr. Zbyněk Pawlas, Ph.D. (25.02.2021)
Lecture+exercises.
Last update: doc. RNDr. Zbyněk Pawlas, Ph.D. (25.02.2021)
Přednáška+cvičení.
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