2024-2025 / MATH2022-1

Monte Carlo methods in statistics

Duration

24h Th, 12h Pr, 40h Proj.

Number of credits

 Master MSc. in Data Science, professional focus (Even years, organized in 2024-2025) 5 crédits 
 Master MSc. in Data Science and Engineering, professional focus (Even years, organized in 2024-2025) 5 crédits 
 Master in mathematics, research focus (Even years, organized in 2024-2025) 8 crédits 
 Master in mathematics, teaching focus (Even years, organized in 2024-2025) 8 crédits 

Lecturer

Arnout Van Messem

Language(s) of instruction

English language

Organisation and examination

Teaching in the second semester

Schedule

Schedule online

Units courses prerequisite and corequisite

Prerequisite or corequisite units are presented within each program

Learning unit contents

The course covers (a selection of) the following topics:

1 Introduction

2 Models and challenges

3 Generating random variables

4 Generating random processes 

5 Monte Carlo Integration and Optimization 

6 Markov Chain Monte Carlo

7 Statistical analysis of simulation data 

8 Variance reduction

 

Learning outcomes of the learning unit

This course contributes to the learning outcomes I.1, I.2, I.3, II.1, IV.4, VI.1, VII.2, VII.4 of the MSc in data science and engineering.

 

A good understanding of the problematics related to simulation and sampling.

 

Prerequisite knowledge and skills

To follow this course it is mandatory to have solid foundations in

  • probability theory (probability measure, probability distributions both uni and multi-variate, CLT, Law of large numbers, ...)
  • parametric statistics (likelihood, Fisher information, statistical tests, confidence intervals, ...)
Working knowledge of Markov chains and processes is an asset.

 

Reference for the basics :

Casella, George, and Roger L. Berger. Statistical inference. Vol. 2. Pacific Grove, CA: Duxbury, 2002.

 

 

Planned learning activities and teaching methods

The course is offered through online videos which the student can watch at his/her own pace. It consists of theory sessions as well as practical sessions (both written and on computer). Q&A sessions will be organized regularly.

 

Mode of delivery (face to face, distance learning, hybrid learning)

Blended learning


Additional information:

Classes will be given through online videos.


Q&A sessions will be organized regularly. Details will be given on the eCampus platform.


 

 

 

 

Course materials and recommended or required readings

All information (course notes, project and exercise sheets, videos) will be made available through platform. 


References

Kroese, Dirk P., Thomas Taimre, and Zdravko I. Botev. Handbook of Monte Carlo Methods. Vol. 706. John Wiley & Sons, 2013.

Robert, Christian, and George Casella. Monte Carlo Statistical Methods. Springer Science & Business Media, 2013.

Robert, Christian P., George Casella, and George Casella. Introducing monte carlo methods with R. Vol. 18. New York: Springer, 2010.

 

 

Exam(s) in session

Any session

- In-person

oral exam

Written work / report


Additional information:

The evaluation of the course happens through the completion of an individual project.

If desired, an oral continuation of the exam is possible. The oral examination can change the final grade up to 2 points, either positive or negative. The oral continuation will consist of one theoretical question and one question/clarification on the completed project.

 

 

 

 

 

 

Work placement(s)

Organisational remarks and main changes to the course

Contacts

Professeur: Arnout Van Messem

 

Association of one or more MOOCs