Lecturer
Dr. Marco Oesting

Teaching assistant
Orkun Furat, M.Sc.

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Time and Place

Lecture
Tuesday, 12 - 14, Heho 18, room 120

Excercise session
Wednesday, 14 - 16, N24, room 131 (biweekly)

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Type

2 hours lecture and 1 hour excercise

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Prerequisites

The audience is supposed to be familiar with basic probability (equivalent to the course "Elementare Wahrscheinlichkeitsrechnung und Statistik").

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Intended Audience

Master Students in any mathematical program of studies.

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Contents

Point processes are popular statistical models for point patterns in space. They have applications in various fields such as astronomy, biology, economics, forestry, geography, materials science or seismology. This course gives an introduction to their general theory with a particular focus on Poisson point processes and related models.

Main topics include:

• basic properties and characteristics of point processes
• special classes of point processes
• Palm distribution
• marked point processes

 

 

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Exercise sheets

 The exercise sheets and scores will be published on Moodle.

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Requirements for the final exam

Successful work out of at least 50% of the exercises in the exercise sheets.

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Exam

There will be an oral exam at the end of the term.

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Literature

• Sung Nok Chiu, Dietrich Stoyan, Wilfrid S. Kendall & Joseph Mecke. Stochastic Geometry and its Applications. 3rd Edition. Wiley, Chicester, 2013.
• Noel Cressie. Statistics for Spatial Data. Revised Edition. Wiley, New York, 2015.
• Daryl J. Daley & David Vere-Jones. An Introduction to the Theory of Point Processes.
  Volume I: Elementary Theory and Methods. 2nd Edition. Springer, New York, 2003.
• Daryl J. Daley & David Vere-Jones. An Introduction to the Theory of Point Processes.
  Volume II: General Theory and Structure. 2nd Edition. Springer, New York, 2008.
• Alan E. Gelfand, Peter J. Diggle, Montserrat Fuentes & Peter Guttorp (Editors). Handbook of Spatial Statistics. Chapman & Hall/CRC, Boca Raton, 2010.
• John F. C. Kingman. Poisson Processes. Oxford University Press, Oxford, 1993.
• Volker Schmidt. Raumliche Statistik. Lecture Notes, Universitat Ulm, Summer term 2011 (in German).

Link to the course reserve of the library.