Time and venue

Lecture:
Mondays, 8–10, HeHo18 E20

Exersice:
Thursdays, 12–14, HeHo18 E20, fortnightly

Length

2 hours lecture + 1 hour exercise
Credit points: 4

Theoretical background

Lectures: Probability Theory, Calculus

Target audience

Master’s in Mathematics and Management, Mathematical Biometry, Teacher Education in Mathematics

Content

This course focuses on the stochastic modelling, statistical analysis and simulation of point patterns in d-dimensional Euclidean space. The techniques presented open up potential applications for a wide range of spatial datasets.

Key topics of the lecture are:

• Poisson point process
• Palm theory
• Gibbs model
• Cox process
• Compound Poisson process
• Convergence of point processes
• Determinantal and permanental point processes

The lecture will be delivered in English.

Lecture notes

The (English) lecture notes can be found on Moodle; subject to ongoing changes.

Criteria for achieving the prerequisite

To be announced

Examination

Admission to the examination is conditional upon having passed the prerequisite (see above). The examination is conducted individually and orally (in German or English as required); dates must be arranged individually.

Exercise sheets 

The exercise sheets and marks achieved will be published on Moodle.

Literature

• Adrian Baddeley, Ege Rubak, Rolf Turner. Spatial Point Patterns: Methodology and Applications with R. Chapman & Hall/CRC, 2015.
• Andrew D. Barbour, Lars Holst, Svante Janson. Poisson Approximation. Clarendon Press, 1992.
• Sung Nok Chiu, Dietrich Stoyan, Wilfrid S. Kendall, Joseph Mecke. Stochastic Geometry and Its Applications. Wiley, 3rd ed., 2013.
• Daryl J. Daley, David Vere-Jones. An Introduction to the Theory of Point Processes. Volume I: Elementary Theory and Methods. Springer, 2nd ed., 2003.
• Daryl J. Daley, David Vere-Jones. An Introduction to the Theory of Point Processes. Volume II: General Theory and Structure. Springer, 2nd ed., 2008.
• J. Ben Hough, Manjunath Krishnapur, Yuval Peres, Bálint Virág. Zeros of Gaussian Analytic Functions and Determinantal Point Processes. American Mathematical Society, 2009.
• Janine Illian, Antti Penttinen, Helga Stoyan, Dietrich Stoyan. Statistical Analysis and Modelling of Spatial Point Patterns. Wiley, 2008.
• Olav Kallenberg. Random Measures, Theory and Applications. Springer, 2017.
• John F. C. Kingman. Poisson Processes. Oxford University Press, 1992.
• Günter Last, Mathew Penrose. Lectures on the Poisson Process. Cambridge University Press, 2017.
• Jesper Møller, Rasmus P. Waagepetersen. Statistical Inference and Simulation for Spatial Point Processes. Chapman & Hall/CRC, 2004.
• Sidney I. Resnick. Extreme Values, Regular Variation, and Point Processes. Springer, 1987.
• Ken’ichi Satō. Lévy Processes and Infinitely Divisible Distributions. Cambridge University Press, 2013.