NMAK24010U Topics in Statistics

Volume 2025/2026
Education

MSc Programme in Statistics

MSc Programme in Mathematics-Economics

Content

The aim of the course is to introduce modern simulation methods. This course concentrates on Markov chain Monte Carlo (MCMC) methods. Examples of applications of these methods to complex inference problems will be given.

 

The course will cover:

  • Metropolis-Hastings algorithm
  • Gibbs sampling
  • Slice sampling
  • Tempering/annealing
  • Hamiltonian Monte Carlo
Learning Outcome

Knowledge:

  • Principles and theory behind the Metropolis-Hastings algorithm and Gibbs sampling
  • Key concepts of slice sampling and how it compares to other MCMC methods
  • Insights into tempering/annealing for overcoming multimodal posteriors
  • Fundamentals of Hamiltonian Monte Carlo, including its advantages in high-dimensional spaces
  • Common challenges such as convergence diagnostics and autocorrelation in MCMC simulations
  • Applications of MCMC methods to complex inference problems in Bayesian statistics


Skills: Ability to

  • Design and implement MCMC algorithms for various statistical models
  • Apply Metropolis-Hastings, Gibbs sampling, slice sampling, and Hamiltonian Monte Carlo to practical problems
  • Analyze and diagnose convergence issues in MCMC simulations using trace plots and statistical tests
  • Compare different MCMC methods in terms of computational efficiency and statistical performance


Competences: Ability to

  • Critically assess the suitability of different MCMC algorithms for a given statistical problem
  • Evaluate the performance of an MCMC method, including its convergence and mixing properties
  • Present complex concepts related to MCMC theory and applications clearly and effectively
It is advantageous to have done Statistics A to fully appreciate the results of the course.

Experience with theoretical statistics at the level of Statistics B and measure theoretic probability (e.g. at the level of Sand and Sand2) is beneficial but not required.
4 hours of lectures per week for 7 weeks.
3 hours of exercises once per 2 weeks for 6 weeks.
  • Category
  • Hours
  • Lectures
  • 28
  • Preparation
  • 168
  • Exercises
  • 9
  • Exam
  • 1
  • Total
  • 206
Oral
Credit
7,5 ECTS
Type of assessment
Oral examination, 30 minutes (30-minute preparation time)
Aid
All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
Several internal examiners
Re-exam

Same as the ordinary exam

Criteria for exam assesment

The student should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.