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 F0 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
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.

Office hours:

  • TBA

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.

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)
F01.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)
F02.pdf
w2/46Mon12/11L3 Spatial models II:
Classic Kriging and covariance estimation (LS)
(HS: 2.3, 2.8, 3)
F03.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)
F04.pdf
Fri16/11L5 Markov fields I:
Gaussian fields
(HS: 12.1.1-12.1.4, 12.1.7)
F05.pdf
w3/47Mon19/11L6 Markov fields II:
Gaussian fields
(SST: 6-6.1; HS: 13.2)
F06.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)
F07.pdf
w4/48Mon26/11L8 Markov fields III:
Spectral representation and Matern-like precision models
(SST: 6.4-6.5)
GMRFs and SPDEs (pdf)
F07.pdf
C3 Gaussian Markov random fields lab3.pdf
Fri30/11L9 Classification
SVD example: svd_fmri.m (fmri.mat)
F09.pdf
w5/49Mon3/12L10 Gibbs-sampling and parameter estimation
(SST: 4-4.5.1)
F10.pdf
C4 Work on HA2
Fri7/12L11 Markov fields III:
Discrete fields
(HSS: 12.1.8)
F11.pdf
w6/49Mon10/12L12 Markov fields IV:
Parameter estimation for discrete fields
(HSS: 12.1.9)
F12.pdf
C5 Discrete field simulation and estimation lab5.pdf
Fri14/12L13 Comments regarding Projects 1 and 2; Thesis projects
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 6, 2018 at 15:15 in MH:309A
Lectures: Monday
15-17, MH:309A
Tuesday 14/11
15-17, MH:309A
Friday
10-12, E:C
Computer exercises: v2-v7:
Wed. 9-12 MH:140
Fri. 13-16 MH:140
Office hours:
Lecturer: Johan Lindström
046-222 40 60
MH:319
Teaching assistants: Elin Olofsson

Official Course Description

CEQ

CEQ - Spatial Statistics