Spatial Statistics and Markov Chain Monte Carlo Methods

2019/2020

Prerequisite/Recommended prerequisite for participation in the module

The module builds on knowledge obtained by the module Statistical Inference for Linear Models from the Bachelor of Science (BSc) in Engineering (Mathematical Engineering)

Content, progress and pedagogy of the module

The course deals with Markov chain Monte Carlo methods as well as one or more of the three main topics within spatial statistics.

Learning objectives

Knowledge

  • know the fundamental models and methods within the chosen main topics (geostatistics, lattice processes or spatial point processes) as well as Markov chain Monte Carlo.
  • have knowledge about the following subjects within the chosen main topic(s)
    • Geostatistics:
      Theory for second order stationary processes, variograms/covariograms, prediction and kriging, as well as model based geostatistics
    • Lattice processes:
      Markov fields, Brook's factorisation and Hammersley-Clifford's theorem and likelihood based statistical analysis
    • Spatial point processes:
      Poisson processes, Cox processes and Markov point processes, as well as statistical analyses based on non-parametric methods (summary statistics) and likelihood based methods
    • Markov chain Monte Carlo:
      Fundamental theory of Markov chains with a view to simulation, Markov chain Monte Carlo methods for simulation of distributions, including the Metropolis-Hastings algorithm and the Gibbs sampler

Skills

  • are able to explain the main theoretical results from the course
  • are able to perform statistical analyses of concrete datasets
  • are able to simulate the examined models

Competences

  • are able to interpret a spatial statistical model in relation to a concrete dataset and give an account of the limitations of the model with respect to describing the variation in the dataset using the theoretical results within spatial statistics
  • are able to simulate distributions using Markov chain Monte Carlo methods and evaluate the output of the Markov chain

Type of instruction

As described in §17.

Extent and expected workload

This is a 5 ECTS course module and the work load is expected to be 150 hours for the student.
 

Exam

Prerequisite for enrollment for the exam

  • For students on the master level: In order to participate in the exam, students must have actively participated in course progress by way of one or several independent oral and/or written contributions.

Exams

Name of examSpatial Statistics and Markov Chain Monte Carlo Methods
Type of exam
Written or oral exam
Individual oral or written exam, or individual ongoing evaluation.
ECTS5
AssessmentPassed/Not Passed
Type of gradingInternal examination
Criteria of assessmentAs stated in the Joint Programme Regulations.
http:/​/​www.engineering.aau.dk/​uddannelse/​Studieadministration/​

Facts about the module

Danish titleRumlig statistik og markovkæde Monte Carlo metoder
Module codeF-MAT-B6-9
Module typeCourse
Duration1 semester
SemesterSpring
ECTS5
Language of instructionDanish and English
Empty-place SchemeYes
Location of the lectureCampus Aalborg
Responsible for the module

Organisation

Study BoardStudy Board of Mathematics, Physics and Nanotechnology
DepartmentDepartment of Mathematical Sciences
FacultyFaculty of Engineering and Science