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# Details for Course FMSN20F Spatial Statistics with Image Analysis

General
• FMSN20F
• Temporary
Course Name
• Spatial Statistics with Image Analysis
Course Extent
• 7.5
Type of Instruction
• Course given jointly for second and third cycle
• 7152 (Centre of Mathematical Sciences / Mathematical Statistics)
• 2020-05-19
• Professor Thomas Johansson

## Current Established Course Syllabus

General
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.

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.
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.
Types of Instruction
• Lectures
• Laboratory exercises
• Project
Examination Formats
• Written report
• Seminars given by participants
• Failed, pass
• At least one course of FMSF15 Markov processes or FMSF10 Stationary stochastic processes. Matlab proficiency.
Assumed Prior Knowledge
Selection Criteria
Literature
• Gelfand, A., Diggle, P. & Guttorp, P.: Handbook of Spatial Statistics. CRC Press Inc, 2010.
Further Information
Course code
• FMSN20F
• 2020-05-19
• Professor Thomas Johansson

## All Established Course Syllabi

1 course syllabus.

Valid from First hand in Second hand in Established
Autumn 2020 2020‑05‑19 10:26:02 2020‑05‑19 10:28:18 2020‑05‑19

## Current or Upcoming Published Course Occasion

No matching course occasion was found.

## All Published Course Occasions

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