Random Fields: Mathematical Theory & Spatial Statistics Applications


Associate Professor Andriy Olenko, La Trobe University


The course surveys the theory of spatial stochastic processes and statistics models, and their applications to a wide range of data including GIS (geographic information systems). It will cover the methodology for spatial modelling, estimation and prediction, and spectral analysis of spatial processes.

Course Overview

The first part of the course covers various topics in the theory of random fields (stochastic processes indexed by points of multidimensional spaces or manifolds). Spectral and correlation properties of random fields will be studied. Gaussian spatial processes and several extensions to non-Gaussian and spatial-temporal scenarios will be covered. Smoothness and other geometric properties of random fields will be investigated.

The second part is devoted to the methodology and applications in spatial modelling. Random fields will be main tools for various types of statistical analysis, estimation, spatial prediction and experimental design. All the methods presented in this part will be introduced in the context of specific real-world data using R software.


A good knowledge of undergraduate probability, statistics and calculus. Familiarity with the software package R would be very useful but not essential.


Four assignments worth 10% each, plus an exam worth 60%. This exam will be held at the students home institution.

Resources/pre-reading (if available)

Lecture notes will be available.

Familiarity with basic theory of second-order stochastic processes will be of help, for example:

  • W.Feller. An Introduction to Probability Theory and Its Applications, Vol. 2, Chapter XIX, sections 1-3.

Learn basics of R programming using some free online R tutorials, for example:

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Associate Professor Andriy Olenko,
La Trobe University

Dr Andriy Olenko is an associate professor in statistics at La Trobe University. He has been with the Department of Mathematics & Statistics at La Trobe since 2007. His research interests include random fields theory, spatial statistics, stochastic approximation, asymptotic theory for long-memory data and applied statistics.