Spatial Statistics with Image Analysis
Spatial statistik med bildanalys

FMSN20F, 7.5 högskolepoäng

Gäller från och med: Autumn 2020
Beslutad av: Professor Thomas Johansson
Datum för fastställande: 2020-05-19

Allmänna uppgifter

Avdelning: Mathematical Statistics
Kurstyp: Gemensam kurs, avancerad nivå och forskarnivå
Kursen ges även på avancerad nivå med kurskod: FMSN20
Undervisningsspråk: English

Syfte

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.

Mål

Kunskap och förståelse

För godkänd kurs skall doktoranden

• 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.

Färdighet och förmåga

För godkänd kurs skall doktoranden

• 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.

Värderingsförmåga och förhållningssätt

För godkänd kurs skall doktoranden

• 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.

Kursinnehåll

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.

Kurslitteratur

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

Kursens undervisningsformer

Undervisningsformer: Föreläsningar, laborationer, projekt

Kursens examination

Examinationsformer: Skriftlig rapport, seminarieföredrag av deltagarna
Betygsskala: Underkänd, godkänd
Examinator:

Antagningsuppgifter

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

Kurstillfällesinformation

Kontaktinformation och övrigt

Kursansvariga:
Hemsida: www.maths.lth.se/matstat/kurser/fmsn20/