Course syllabus for Spatial statistics and image analysis

Course syllabus adopted 2026-02-26 by Head of Programme (or corresponding).

Overview

  • Swedish nameSpatial statistik och bildanalys
  • CodeTMS016
  • Credits7.5 Credits
  • OwnerMPENM
  • Education cycleSecond-cycle
  • Main field of studyMathematics
  • DepartmentMATHEMATICAL SCIENCES
  • GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail

Course round 1

  • Teaching language

    English

  • Application code

    20145

  • Open for exchange students

    Yes

Credit distribution

Module
Sp1
Sp2
Sp3
Sp4
Summer
Not Sp
Examination dates
0101 Examination 7.5 c
Grading: TH		 7.5 c

In programmes

Examiner

Eligibility

General entry requirements for Master's level (second cycle)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements

Specific entry requirements

English 6 (or by other approved means with the equivalent proficiency level)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements

Course specific prerequisites

One basic course in mathematical statistics as well as MVE170 or a similar course on stochastic processes.

Aim

The aim of the course is to provide basic knowledge of models and methods with practical applications in spatial statistics and image analysis.

Learning outcomes (after completion of the course the student should 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 statistical methodology, results and conclusions, both in written and oral form.

Content

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

Organisation


Lectures and exercise sessions/computer labs.

Literature

The course literature will be announced no later than 12 weeks before the start of the course

Examination including compulsory elements

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

The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers about disability study support.

Spatial statistics and image analysis | Chalmers