2020-2021 / MATH2022-2

Large sample analysis : theory and practice, General course

Duration

24h Th, 12h Pr, 10h Proj.

Number of credits

 Master in mathematics (120 ECTS)8 crédits 
 Master in mathematics (60 ECTS)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

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

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

Ex cathedra teaching, exercise sessions (both on computer and on paper). An end of term assignement is planned, though the precise modalities still need to be fixed.

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

face-to-face

Organisational adjustments related to the current health context

distance learning

Recommended or required readings

All information (course notes, project and exercise sheets) will be made available via the eCampus platform. 

Références
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.

Assessment methods and criteria

Below you will find information on the evaluation methods planned for in-person and remote exams as well as those planned for hybrid sessions. Depending on how the health crisis evolves, the chosen method will be communicated to you no later than one month before the start of the exam session.

Any session :

- In-person

oral exam

- Remote

written work

- If evaluation in "hybrid"

preferred remote


Additional information:

Evaluation of the course happens through the completion of an individual project.
If requested, an oral continuation of the exam is possible (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)

Organizational remarks

Contacts

Professeur: Arnout Van Messem
 
Assistant: Carole Baum