FOR063F, Statistical Methods and Simulation (7.5 hp)

Course Plan: Statistical Methods and Simulation (7.5 hp)

ECTS/HP: 7.5

Course code: FOR063F

Educational level: Third-cycle course

Entry Requirements

Knowledge of statistics corresponding to an introductory course in statistics for engineers. Some familiarity with programming in MATLAB, R, or Python is recommended, but not required.

Course Contents

The course provides the necessary background to understand statistical methods based on Markov Chain Monte Carlo (MCMC). It also offers participants an opportunity to enhance their ability to apply statistical methods more broadly. Topics covered include fundamental concepts of inference, including Bayesian inference, methods for generating random numbers from probability distributions (such as the inverse transform and rejection sampling methods), integral estimation using Monte Carlo simulation, finite Markov chains, ergodicity in finite Markov chains, and an introduction to MCMC methods, including the Metropolis-Hastings algorithm.

Learning outcomes: Upon successful completion, participants will be able to

• apply basic statistical methods with increased confidence.
• Explain basic concepts from Bayesian inference and perform Bayesian updating.
• Apply the methods for generating random numbers that the course covers.
• Compute integrals using random sampling.
• work with basic concepts from the theory of finite Markov chains, in particular concepts relating to stationary distributions.
• Apply MCMC methods using software

Course methods

The course consists of seminars where each session begins with a lecture, followed by group work on a set of exercises. These exercises are both theoretical and computer-based. The four mandatory home assignments are closely linked to the exercises. Additionally, four of the seminars are problem seminars, where participants present solutions to randomly selected problems from the home assignments.

Examination form: The course includes four home assignments and a final exam. However, students who attend the problem seminars can earn up to full credit on the final exam, in which case the exam is waived.

Textbook / Main Resource:

• Olle Häggström's book "Finite Markov Chains and Algorithmic Applications"

Additional Resources

Sheldon Ross, “Simulation”, sixth edition.

Douglas C. Montgomery, “Design and Analysis of Experiments”, sixth edition

Period: Sp 1-2, 2026

Send application to: Adam Jonsson, Email: adam.jonsson@ltu.se, 0920-491948

Deadline for application: August 1 2026.

Limited number of students: The first 25 applicants.

Tuition: No tuition fee for doctoral students in Swedish universities

Contact person: Adam Jonsson, Email: adam.jonsson@ltu.se, 0920-491948

Examiner: Peter Wall

Course syllabus decided by: Lars-Göran Westerberg, Head of PhD studies at TVM

Date of decision: 2026-02-18