Institute of Stochastics

Spatial Statistics

This lectures organization takes place via Moodle.

Lecturer

Prof. Dr. Evgeny Spodarev

Teaching assistants

Ly Viet Hoang & Artur Bille

 

Time and Place

Lecture

Monday, 12:15 - 13:45 pm in E60 (Heho 18)
Wednesday, 10:15 - 11:45 am in E60 (Heho 18)
Monday, 01.05.2023 (International Workers' Day) --> Friday, 28.04.2023, 08:15 - 09:45 am in E60 (Heho 18)
Monday, 29.05.2023 (Whit Monday) --> Friday, 02.06.2023, 08:15 - 09:45 am in E60 (Heho 18)

Exercise session

Friday, 10:15 - 11:45 am in E60 (Heho 18)­

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Type of lecture

4 ho­urs of lecture and 2 hours of exercise

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­Prerequisites

  • Calculus
  • Probability Calculus 
  • Probability Theory and Stochastic Processes

Recommended, but not necessary: Measure Theory and Random Fields.

 

Intended Audience

Master students in Mathematik, Wirtschaftsmathematik, Mathematische Biometrie,  Finance and Lehramt Mathematik.

 

Content 

The lecture is devoted to the theory of statistical inference and prediction of stationary random fields which model rough surfaces in nature and technology. The lecture focuses on the application of statistical methods to data in R. Possible areas of application include (but are not limited to) geosciences (geological prediction of ore and fossil energy ressources), climate research (weather forecasts), and extreme value theory, to name just a few. 

Topics:

  • Estimation of the mean, covariance function, spectral density
  • Prediction of discrete random fields based on random mosaics
  • Different forms of kriging (simple, ordinary, etc.)
  • Geoadditive regression with bi-splines
  • Spatial quantile regression
  • Prediction based on excursion metrics
  • Extrapolation of max-stable random fields  

 

 

Lecture notes

The latest version of the lecture notes can be downloaded here. The script is continuously updated and corrected. Notes and comments are highly appreciated and should be communicated to the lecturer or the teaching assistants via email.
Useful notes of other lectures:

 

Exam

There will be an oral exam. The exam date must be agreed individually with Prof. Spodarev. To participate in the exam, it is necessary to earn at least 50% of the points of all problem sheets. 

 

Problem sheets

Problem sheets can be downloaded in the Moodle course.

 

Literature

  • Spodarev, E., ed.: Stochastic geometry, spatial statistics and random fields. Asymptotic methods. LNM, volume 2068, Springer, 2013.
  • Schmidt, V., ed.: Stochastic geometry, spatial statistics and random fields. Models and algorithms. LNM, volume 2120, Springer, 2015.
  • Fahrmeir, L., Kneib, T., Lang, S., Marx, B. Regression: Modelle, Methoden und Anwendungen. 2nd ed., Springer, 2022 
  • Ivanov, A.V., Leonenko, N.N.: Statistical Analysis of Random Fields, Kluwer, 1989
  • Ramm, A.: Random Fields Estimation, World Scientific, 2005
  • Yaglom, A. M.: Correlation Theory of Stationary and Related Random Functions, Volume I,II Springer, 1987

Contact

Lecturer

Prof. Dr. Evgeny Spodarev

Office hours: by appointment per email.

Homepage

Teaching assistants

Ly Viet Hoang & Artur Bille

Office hours: by appointment per e-mail.

Homepage

Notes