(Created 2011-09-01.)
 SPATIAL STATISTICS WITH IMAGE ANALYSIS FMSN20
Credits: 7,5. Grading scale: TH. Cycle: A (Second Cycle). Main field: Technology. Language of instruction: The course will be given in English on demand. FMSN20 overlaps following cours/es: FMS150, MAS228 and MASM13. Optional for: C5, D5, D5bg, E5, E5bg, E5mt, F5, F5bg, F5mt, Pi4, Pi4mrk, Pi4ssr. Course coordinator: Director of studies, Anna Lindgren, studierektor@matstat.lu.se, Mathematical Statistics. Recommended prerequisits: A basic course in mathematical statistics and, additionally, a course in Image analysis or at least one course in Markov processes or Stationary stochastic processes. Matlab proficiency. The course might be cancelled if the number of applicants is less than 16. Assessment: Written and oral project presentation. Further information: The course is also given at the faculty of science. Home page: http://www.maths.lth.se/matstat/education/.

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.