Lecturer

Prof. Dr. Evgeny Spodarev

Teaching Assistant

Dr. Michael Juhos

Time and Place

Lecture

Monday, 12:00–14:00, N24 131
Thursday, 12:00–14:00, N24 226

Exercise

Monday, 14:00–16:00, N24 131

Schedule

4 hours lecture and 2 hours exercises

Requirements

• Analysis,
• Elementary Probability and Statistics,
• Probability Theory and Stochastics Processes.

It is recommended that you have attended Measure Theory and Random Fields.

Target groups

Master’s degree in Mathematics and Business Mathematics, Mathematical Biometrics, Teaching qualification in Mathematics, Finance

Contents

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 constantly being expanded and corrected.
Notes and comments are very welcome and should be sent via email to the lecturer or trainer.
Lecture notes for related lectures:

• Random Fields.

Exam

There will (likely) be an oral exam.
Appointments are to be agreed individually with Prof. Spodarev.
The prerequisite for taking the exam is to achieve at least 50 % of the practice points.

Exercise Sheets

The exercise sheets can be found 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. Volumes I, II, Springer, 1987