# 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.

### Choose semester and course offering

Choose semester and course offering to see information from the correct course syllabus and course offering.

Headings with content from the Course syllabus SF2955 (Spring 2022–) are denoted with an asterisk ( )

## 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.

### Course disposition

No information inserted

## 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

No information inserted

### Equipment

No information inserted

### 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.

A, B, C, D, E, FX, F

### 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

No information inserted

### Opportunity to raise an approved grade via renewed examination

No information inserted

### 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.

## Further information

### Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web SF2955

Mathematics

Second cycle