Spatial Statistics and Image Analysis

The course can be part of the following programmes: 1) Mathematical Sciences, Master's Programme (N2MAT) and 2) Bachelor's Programme in Mathematics (N1MAT).

Knowledge corresponding to thecourses MSG110 (Probability theory) and MSG800 (Basic stochastic processes).

• Spatial data types: geostatistical data, areal unit data and spatial point patterns.
• Random fields and random field models for spatial data.
• Stationarity concepts, covariance functions and related quantities.
• Areal data models and lattice-based autoregressive spatial models.
• Markov random fields, Gibbs distributions and local dependence structures.
• Spatial point processes, including Poisson, Cox and Markov point process models.
• Statistical inference for spatial models, including likelihood-based, pseudolikelihood-based and simulation-based methods.
• Variogram/covariance analysis and spatial prediction using kriging.
• Statistical models for image data and image analysis.
• Model-based methods and computational approaches for image reconstruction and analysis.

On successful completion of the course, the student shall be able to:

• Formulate and analyse stochastic models for spatially indexed data, including discretely and continuously indexed random fields, and spatial point processes.
• Explain and apply Markov random field models for spatial data and images.
• Perform spatial prediction and interpolation using covariance-based methods such as kriging.
• Perform basic statistical analyses of spatial point pattern datasets.
• Explain and apply different types of image analysis and image processing methodologies.
• Apply frequentist and Bayesian estimation methods in spatial statistics and imaging contexts.
• Implement computational algorithms for spatial statistics and image analysis using appropriate software tools.
• Critically assess modeling assumptions and inference methods for real-world spatial and imaging data.
• Clearly communicate methodology, results and conclusions within the field, both in written and oral form.

Lectures and exercise sessions/computer labs.

Language of instruction: English

The assessment is based on a written exam and project work.

If a student who has failed the same examined component twice wishes to change examiner before the next examination, a written application shall be sent to the department responsible for the course and shall be granted unless there are special reasons to the contrary (Chapter 6, Section 22 of the Higher Education Ordinance).

The grading scale comprises: Pass with Distinction (VG), Pass (G) and Fail (U).

At the end of the course, the students will be asked to answer a questionnaire. The results from the evaluation and potential changes to the course will be shared with students who participated in the evaluation and students who are starting the course.