SF2955 Computer Intensive Methods in Mathematical Statistics 7.5 credits
The overall purpose of the course is to give basic knowledge, understanding and ability to solve problems in areas of statistical inference where very few and simple assumptions are made as to how data have been generated, and to be able to use computers to perform the extensive calculations that are often required.
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Application
For course offering
Spring 2025 Start 17 Mar 2025 programme students
Application code
61213
Content and learning outcomes
Course contents
This course provides an introduction to modern Monte Carlo simulation and its applications to mathematical statistics.
Sequential Monte Carlo (SMC) methods (alternatively termed particle filters) form a class of genetic-type sampling techniques that simulate recursively from sequences of probability distributions. These methods are widely used in a variety of engineering and scientific disciplines such as signal processing, robotics, and financial mathematics.
Markov chain Monte Carlo (MCMC) methods constitute a collection of simulation techniques that use cleverly selected Markov chains to generate samples from complicated, possibly high-dimensional distributions. MCMC is successfully applied in Bayesian statistical methods—which allow prior knowledge to be included in the inferential analysis—but also areas like optimization, statistical mechanics, and machine learning.
Intended learning outcomes
After completing the course, the student shall be able to
- formulate and apply Monte Carlo simulation techniques,
- apply Monte Carlo simulation to frequentist and Bayesian statistics,
- design and implement an SMC algorithm simulating from a given sequence of probability distributions, and
- design and implement an MCMC algorithm simulating from the posterior distribution of a complex Bayesian model and analyse the output.
Literature and preparations
Specific prerequisites
- English B / English 6
- Completed basic course in mathematical statistics (SF1918, SF1922 or equivalent).
- Completed basic course in numerical analysis (SF1544, SF1545 or equivalent)
Recommended prerequisites
Equipment
Literature
Englund, Gunnar. Datorintensiva metoder i matematisk statistik. Compendium from KTH.
Material from the department of Mathematics.
Examination and completion
If the course is discontinued, students may request to be examined during the following two academic years.
Grading scale
Examination
- OVNA - Assignments, 3.0 credits, grading scale: P, F
- TENA - Examination, 4.5 credits, grading scale: A, B, C, D, E, FX, F
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
Opportunity to complete the requirements via supplementary examination
Opportunity to raise an approved grade via renewed examination
Examiner
Ethical approach
- All members of a group are responsible for the group's work.
- In any assessment, every student shall honestly disclose any help received and sources used.
- In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.