Mathematical Sciences

Lund University

Spatial Statistics with Image Analysis, HT18


First lecture on November 5:th 15.15-17.00 in MH:309A

Introductory lecture L00-1x3.pdf given at the Image analysis (FMA170) course on 2018-10-11.


Three home assignments/projects. The assignments will be handed out during the 2:nd, 4:th and 6:th course week.

v2: 1)Classic Kriging (proj1.pdf)
Comments regarding home assignment 1:
  • Don't forget to add the nugget to the covariance matrix!
  • For the Universal Kriging it might be hard to estimate shape parameters (matern and cauchy). Check behaviour for different nu or kappa and try fixing nu or kappa if you're having trouble.
Data: swissRainfall.mat
Handed out 2018-11-12, due 2018-11-27 23:59.

v4: 2) Gaussian Markov fields and non-Gaussian observations
Handed out 2018-11-26, due 2018-12-11 23:59.

v6: 3) MRFs, classification, and space-time data
Handed out 2018-12-10, due 17:00 the day before your presentation.
Written and oral presentation of project 3.

Presentation times:

Presentations are 10 minutes (NOT longer). Either bring your own computer and VGA/HDMI-adapter or "bring" a pdf-presentation per email (to Johan) or on a USB-stick.


Most of the material is coverd in:

Both available as E-books from the Lund University Libraries.

Usefull formula for matrix manipulations can be found in:

Chapters 6.2 Expectation of Linear Combinations; 8.1 Gaussians:Basics; 9.1 Block matrices; and 9.6 Positive Definite and Semi-definite Matrices are of special relevans.


Recommended reading in parentheses (HS:? - Chapters in the Handbook of Spatial Statistics; SST:? - Spatial and Spatio-temporal Bayesian Models with R-INLA).

w1/45Mon5/11L1 Introduction:
Statistical modelling
C0 Image data and dependence in Matlab (Work at home) lab0.pdf
Fri9/11L2 Spatial models I:
Random fields and covariance models
(HS: 2.1, 2.2, 2.5-2.7)
Spectral representation
(HS: 5.1-5.2)
w2/46Mon12/11L3 Spatial models II:
Classic Kriging and covariance estimation (LS)
(HS: 2.3, 2.8, 3)
C1 Covariance estimation lab1.pdf
Wen14/11L4 Spatial models III:
Discussion of Lab 1 and covariance estimation (ML and REML estimation)
(HS: 4.1-4.3)
Fri16/11L5 Markov fields I:
Gaussian fields
(HS: 12.1.1-12.1.4, 12.1.7)
w3/47Mon19/11L6 Markov fields II:
Gaussian fields
(SST: 6-6.1; HS: 13.2)

C2 Work on HA1
Fri23/11L7 Hierarchical models II:
Bayesian analysis
(HS: 7.1-7.3; SST: 3-3.5)
Non-Gaussian data
(HS: 7.4-7.5; SST: 5-5.3, 4.6-4.7)
Approximate inference for latent GMRFs (pdf)
w4/48Mon26/11L8 Markov fields III:
Spectral representation and Matern-like precision models
(SST: 6.4-6.5)
GMRFs and SPDEs (pdf)
C3 Gaussian Markov random fields lab3.pdf
Fri30/11L9 Classification
SVD example:
w5/49Mon3/12L10 Gibbs-sampling and parameter estimation
(SST: 4-4.5.1)
C4 Work on HA2
Fri7/12L11 Markov fields III:
Discrete fields
(HSS: 12.1.8)
w6/49Mon10/12L12 Markov fields IV:
Parameter estimation for discrete fields
(HSS: 12.1.9)
C5 Discrete field simulation and estimation
Fri14/12L13 Comments regarding Projects 1 and 2; Thesis projects
w7/50C6 Work on HA3


A basic course in mathematical statistics, and at least one of:

Recommended related courses (not prerequisits)

Related pages

Course Information

NF Code: MASM25
Level:Advanced Level
First lecture:November 5, 2018 at 15:15 in MH:309A
Lectures: Monday
15-17, MH:309A
Tuesday 14/11
15-17, MH:309A
10-12, E:C
Computer exercises: v2-v7:
Wed. 9-12 MH:140
Fri. 13-16 MH:140
Office hours: Tuesday
15:30-17:00, MH:319
Lecturer: Johan Lindström
046-222 40 60
Teaching assistants: Elin Olofsson
Lovisa Svensson
Beata Torlegård

Official Course Description


CEQ - Spatial Statistics