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

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 image analysis and spatial statistics.

Skills and abilities
For a passing grade the student must

• independently suggest and analyse stochastic models for high-dimensional data, in particular in image analysis and spatial statistics,

• 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, Markov fields, Gibbs distributions, shape analysis. Correlation structures, multivariate techniques, analysis of discrimination. Simulation methods for stochastic inference (MCMC, etc.). Stochastic remote sensing and spatial statistics.

Literature
Lindgren, F: Image Modelling and Estimation - A Statistical Approach, 2006.