Valid for: 2023/24
Faculty: Faculty of Engineering, LTH
Decided by: PLED I
Date of Decision: 2023-04-14
Elective for: F5, F5-fm, I5-fir, Pi5, R5
Language of instruction: The course will be given in English
Advanced dependence modelling in multivariate data analysis is
an important and challenging subject with important applications in
finance, environmental studies and insurance. This course provides
an introduction to parameter mixture distributions, conditional
independence and asymptotic models used to construct multivariate
models in higher dimensions, along with a discussion of why there
is a need to separate the dependence structure from the marginal
distributions.
The course has three main objectives:
Knowledge and understanding
For a passing grade the student must
Competences and skills
For a passing grade the student must
Judgement and approach
For a passing grade the student must
Multivariate distributions including, normal, students-t,
spherical, elliptical and parametric mixture distributions.
Measures of association such as: Pearson’s correlation,
Kendall’s tau, and Spearman’s rho.
Properties of copulas; spherical, elliptical, and Archimedean
copulas; simulation of copulas.
Some theoretical background for univariate extreme value theory and
max-stable distributions in the bivariate case. Methods for
constructing multivariate models in higher dimensions: copula
representations, Sklar’s theorem and the Fréchet-Hoeffding
bounds for joint distributions.
Statistical inference for copulas and multivariate extreme-value
distributions; including multivariate peak over threshold, maximum
likelihood, as well as CFG and Pickand’s non-parametric
estimators.
Grading scale: TH - (U,3,4,5) - (Fail, Three, Four, Five)
Assessment: Written exam and computer labs with written reports.
The examiner, in consultation with Disability Support Services, may deviate from the regular form of examination in order to provide a permanently disabled student with a form of examination equivalent to that of a student without a disability.
Parts
Code: 0121. Name: Written Examination.
Credits: 6. Grading scale: TH. Assessment: Written examination.
Code: 0221. Name: Laboratory Work.
Credits: 1,5. Grading scale: UG. Assessment: Computer exercises and written report.
Assumed prior knowledge: FMSN55 Statistical Modelling of Extreme Values
The number of participants is limited to: No
The course overlaps following course/s: FMSN15, MASM23, MASM33
Director of studies: Johan Lindström, studierektor@matstat.lu.se
Course coordinator: Docent Nader Tajvidi, nader.tajvidi@matstat.lu.se
Course administrator: Susann Nordqvist, expedition@matstat.lu.se
Course homepage: https://www.maths.lu.se/utbildning/civilingenjoersutbildning/matematisk-statistik-paa-civilingenjoersprogram/
Further information: The course is also given at the faculty of science with the course code MASM33.