Subject description - XP01NAM
Summary of Study |
Summary of Branches |
All Subject Groups |
All Subjects |
List of Roles |
Explanatory Notes
Instructions
| XP01NAM | Random sets | ||
|---|---|---|---|
| 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 28.4.2024 09:51:49, 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) |