(Created 2011-09-01.)

SPATIAL STATISTICS WITH IMAGE ANALYSIS | FMSN20 |

**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.

*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.

*Skills and abilities*

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 (MCMC, etc.). Applications in climate, environmental statistics, remote sensing, and spatial statistics.

**Literature**

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