FMSN20F

Tillfällig

Spatial Statistics with Image Analysis

7.5

Gemensam kurs, avancerad nivå och forskarnivå

7152 (Centre of Mathematical Sciences / Mathematical Statistics)

2020-05-19

Professor Thomas Johansson

English

Varje hösttermin

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.

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.

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.

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.

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.

Föreläsningar

Laborationer

Projekt

Skriftlig rapport

Seminarieföredrag av deltagarna

Underkänd, godkänd

At least one course of FMSF15 Markov processes or FMSF10 Stationary stochastic processes. Matlab proficiency.

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

FMSN20F

2020-05-19

Professor Thomas Johansson