Mathematical Sciences

Lund University

Spatial Statistics with Image Analysis, HT18

News

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.

Examination

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
proj1_data.m
Handed out 2018-11-12, due 2018-11-27 23:59.

v4: 2)Gaussian Markov fields and non-Gaussian observations
Comments regarding home assignment 2:
  • Common optimisation misstakes include forgetting one of the determinants and swaping signs. Matlab does minimisation(!) not maximisation.
  • When computing log-determinants use the diagonal elements of the Choleskey-factors. Directly calling log(det(Q)) will result in numerical problems.
Data:HA2_forest.mat
Functions:proj2_data.m
GMRF_negloglike_skeleton.m
GMRF_taylor_skeleton.m
Handed out 2018-11-26, due 2018-12-11 23:59.

v6: 3)MRFs, classification, and space-time data
Data: titan.jpg
fmri.mat
Functions: fmri_ST_init.m
fmri_class_init.m
Handed out 2018-12-10, due 23:59 the day before your presentation.
Written and oral presentation of project 3.

Literature

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.

Schedule

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

DayLecture/ExerciseHandout
w1/45Mon5/11L1 Introduction:
Statistical modelling
(1)
L01-1x3.pdf
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)
L02-1x3.pdf
w2/46Mon12/11L3 Spatial models II:
Classic Kriging and covariance estimation (LS)
(HS: 2.3, 2.8, 3)
L03-1x3.pdf
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)
L04-1x3.pdf
Fri16/11L5 Markov fields I:
Gaussian fields
(HS: 12.1.1-12.1.4, 12.1.7)
L05-1x3.pdf
w3/47Mon19/11L6 Markov fields II:
Gaussian fields
(SST: 6-6.1; HS: 13.2)
L06-1x3.pdf

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)
L07-1x3.pdf
w4/48Mon26/11L8 Markov fields III:
Spectral representation and Matern-like precision models
(SST: 6.4-6.5)
GMRFs and SPDEs (pdf)
L07-1x3.pdf
C3 Gaussian Markov random fields lab3.pdf
Fri30/11L9 Classification
SVD example: svd_fmri.m (fmri.mat)
L09-1x3.pdf
w5/49Mon3/12L10 Gibbs-sampling and parameter estimation
(SST: 4-4.5.1)
L10_notes.pdf (comments regarding Gibbs-sampling for GMMs.)
L10-1x3.pdf
C4 Work on HA2
Fri7/12L11 Markov fields III:
Discrete fields
(HSS: 12.1.8)
L11-1x3.pdf
w6/49Mon10/12L12 Markov fields IV:
Parameter estimation for discrete fields
(HSS: 12.1.9)
L12-1x3.pdf
C5 Discrete field simulation and estimation lab5.pdf
Fri14/12L13 Comments regarding Projects 1 and 2; Thesis projects L13-1x3.pdf
w7/50C6 Work on HA3

Prerequisits

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

Recommended related courses (not prerequisits)

Related pages

Course Information

LTH Code:FMSN20
NF Code: MASM25
Credits:7.5
Level:Advanced Level
Language:English
First lecture:November 5, 2018 at 15:15 in MH:309A
Lectures: Monday
15-17, MH:309A
Friday
10-12, E:C
Computer exercises: v2-v6:
Wed. 9-12 MH:140
Fri. 13-16 MH:140
v7:
Tue. 9-12 MH:140
Wed. 9-12 MH:140
Office hours: Friday (11/1)
13:15-15:00, MH:319
Lecturer: Johan Lindström
046-222 40 60
MH:319
Teaching assistants: Elin Olofsson
Lovisa Svensson
Beata Torlegård

Official Course Description

CEQ

CEQ - Spatial Statistics