Course Syllabus for

Spatial Statistics with Image Analysis Spatial statistik med bildanalys

FMSN20F, 7.5 credits

Valid from: Autumn 2020
Decided by: Professor Thomas Johansson
Date of establishment: 2020-05-19

General Information

Division: Mathematical Statistics
Course type: Course given jointly for second and third cycle
The course is also given at second-cycle level with course code: FMSN20
Teaching language: 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.

Goals

Knowledge and Understanding

For a passing grade the doctoral 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 doctoral 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 doctoral 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.

Course 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.

Course Literature

Gelfand, A., Diggle, P. & Guttorp, P.: Handbook of Spatial Statistics. CRC Press Inc, 2010.

Instruction Details

Types of instruction: Lectures, laboratory exercises, project

Examination Details

Examination formats: Written report, seminars given by participants