Subject description - XP01NAM
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Explanatory Notes
Instructions
XP01NAM | Random sets | ||
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Roles: | Extent of teaching: | 2+2 | |
Department: | 13101 | Language of teaching: | |
Guarantors: | Helisová K. | Completion: | ZK |
Lecturers: | Helisová K. | Credits: | 4 |
Tutors: | Helisová K. | Semester: | L,Z |
Web page:
http://math.feld.cvut.cz/helisova/01XP01NAM.htmlAnotation:
Students get the basic overview on the theory of random sets, their probabilistic models, statistical analyses and applications.Course outlines:
1. | Introduction to random sets | |
2. | Steiner formula | |
3. | Boolean model | |
4. | Contact distribution function, spatial correlation function | |
5. | Shape characteristics | |
6. | Random sets given by a density | |
7. | Quermass-interaction process | |
8. | MCMC simulations of random sets | |
9. | Simulation-based inference | |
10. | Maximum likelihood for random sets | |
11. | Takacs-Fiksel method | |
12. | Marked random sets | |
13. | Digital image analysis | |
14. | Applications of random sets |
Exercises outline:
1. | Introduction to random sets | |
2. | Steiner formula | |
3. | Boolean model | |
4. | Contact distribution function, spatial correlation function | |
5. | Shape characteristics | |
6. | Random sets given by a density | |
7. | Quermass-interaction process | |
8. | MCMC simulations of random sets | |
9. | Simulation-based inference | |
10. | Maximum likelihood for random sets | |
11. | Takacs-Fiksel method | |
12. | Marked random sets | |
13. | Digital image analysis | |
14. | Applications of random sets |
Literature:
1. | Molchanov I. (2005): Theory of Random Sets. Springer Verlag, London. | |
2. | Stoyan D., Kendall W.S., Mecke J. (1995): Stochastic Geometry and Its Applications. Wiley, Chichester. |
Requirements:
Subject is included into these academic programs:Program | Branch | Role | Recommended semester |
Page updated 4.5.2024 15:51:41, semester: Z/2023-4, Z/2024-5, L/2023-4, Send comments about the content to the Administrators of the Academic Programs | Proposal and Realization: I. Halaška (K336), J. Novák (K336) |