Course syllabus

# Spatial statistik med bildanalys Spatial Statistics with Image Analysis

## FMSN20, 7,5 credits, A (Second Cycle)

Valid for: 2020/21
Decided by: PLED I
Date of Decision: 2020-04-03

## General Information

Elective for: BME4, C4, D5-bg, E4-bg, F4, F4-bg, Pi4-ssr, Pi4-biek, Pi4-bam, MMSR2
Language of instruction: The course will be given in English

## Aim

The aim of the course is to provide the student with tools for handling high-dimensional statistical problems. The course contains models, and methods with practical applications, mainly for spatial statistics and image analysis. Of special importance are the Bayesian aspects, since they form the foundation for many modern spatial statistical and image analysis methods. The course emphasises methods with appications in climate, environmental statistics, and remote sensing.

## Learning outcomes

Knowledge and understanding
For a passing grade the student must

• explain and use the concept of a stochastic model, in particular from a Bayesian perspective,
• describe the principles of Bayesian modelling and inference,
• identify and describe stochastic models and analysis methods for high-dimensional problems, in particular regarding spatial statistics and image analysis.

Competences and skills
For a passing grade the student must

• independently suggest and analyse stochastic models for high-dimensional data, in particular in spatial statistics and image analysis,
• independently implement a computer program for the solution of a given statistical problem and relating analysis method,
• present motivations, course of action, and conclusions in the solution of a given statistical problem, both written and orally.

Judgement and approach
For a passing grade the student must

• identify and problemise possibilities and limitations of stochastic modelling and inference, in particular in high-dimensional problems,
• be able to assume a stochastic point of view on random variation in natural phenomena.

## Contents

Bayesian methods for stochastic modelling, classification and reconstruction. Random fields, Gaussian random fields, Kriging, Markov fields, Gaussian Markov random fields, non-Gaussian observationer. Covariance functions, multivariate techniques. Simulation methods for stochastic inference (Gibbs sampling). Applications in climate, environmental statistics, remote sensing, and spatial statistics.

## Examination details

Grading scale: TH - (U,3,4,5) - (Fail, Three, Four, Five)
Assessment: Written and oral project presentation. The final grade is determined by the result of the project parts.

The examiner, in consultation with Disability Support Services, may deviate from the regular form of examination in order to provide a permanently disabled student with a form of examination equivalent to that of a student without a disability.

Parts
Code: 0115. Name: Project Part 1.
Credits: 2,5. Grading scale: UG. Assessment: Written project report
Code: 0215. Name: Project Part 2.
Credits: 5. Grading scale: UG. Assessment: Written and oral project presentation

• FMSF10 Stationary Stochastic Processes or FMSF15 Markov Processes or FMSF20 Mathematical Statistics, Basic Course or FMSF25 Mathematical Statistics - Complementary Project or FMSF45 Mathematical Statistics, Basic Course or FMSF50 Mathematical Statistics, Basic Course or FMSF55 Mathematical Statistics, Basic Course or FMSF70 Mathematical Statistics or FMSF75 Mathematical Statistics, Basic Course

Assumed prior knowledge: At least one course in Markov processes or Stationary stochastic processes. Matlab proficiency.
The number of participants is limited to: No
The course overlaps following course/s: FMS150, MASM13, MASM25