Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-62-15-M-7

Spatial Statistics (M, 4.5 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-62-15-M-7 Spatial Statistics 4.5 CP (135 h)

Basedata

CP, Effort 4.5 CP = 135 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Module Manager
Lecturers
Area of study [MAT-STO] Stochastics/Statistics/Financial Mathematics
Reference course of study [MAT-88.105-SG] M.Sc. Mathematics
Livecycle-State [NORM] Active

Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
2V MAT-62-15-K-7
Spatial Statistics
P 28 h 107 h - - PL1 4.5 irreg.
  • About [MAT-62-15-K-7]: Title: "Spatial Statistics"; Presence-Time: 28 h; Self-Study: 107 h

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: each semester
  • Examination number: 86406 ("Spatial Statistics")

Evaluation of grades

The grade of the module examination is also the module grade.


Contents

  • Spatial point processes (in R² und R³),
  • Point process models (Poisson process, Hard-core and cluster processes, Gibbs processes) and their simulation,
  • Statistical methods for pint processes,
  • Marked point processes and particle processes.

Competencies / intended learning achievements

Upon completion of this module, the students know the basics of the point process theory and of common point process models. They are able to statistically analyze and model point patterns. They understand the proofs presented in the lecture and are able to comprehend and explain them. In particular, they are able to outline the conditions and assumptions that are necessary for the validity of the statements.

The students have developed a skilled, precise and independent handling of the terms, propositions and techniques taught in the lecture. In addition, they have learnt how to apply these techniques to new problems, analyze them and develop solution strategies

Literature

  • J. Møller, R.P. Waagepetersen: Statistical Inference and Simulation for Spatial Point Processes,
  • D. Stoyan, W.S. Kendall, J. Mecke: Stochastic Geometry and its Applications,
  • J. Illian, A. Penttinen, H. Stoyan, D. Stoyan: Statistical Analysis and Modelling of Spatial Point Patterns.

Requirements for attendance (informal)

More advanced knowledge in Stochastics (e.g. from the courses [MAT-60-12-K-4] or [MAT-60-11-K-4]) is useful but not necessarily required.

Modules:

Requirements for attendance (formal)

None

References to Module / Module Number [MAT-62-15-M-7]

Module-Pool Name
[MAT-62-MPOOL-7] Specialisation Statistics (M.Sc.)
[MAT-65-MPOOL-7] Specialisation Image Processing and Data Analysis (M.Sc.)
[MAT-AM-MPOOL-7] Applied Mathematics (Advanced Modules M.Sc.)