24h Th, 12h Pr, 40h Proj.
Number of credits
|Master in data science (120 ECTS)||5 crédits|
|Master in data science and engineering (120 ECTS)||5 crédits|
N..., Yvik Swan
Language(s) of instruction
Organisation and examination
Teaching in the first semester, review in January
Units courses prerequisite and corequisite
Prerequisite or corequisite units are presented within each program
Learning unit contents
CHAPTER I : Generating random samples
1 On randomness
2 Inverse transform sampling
3 Rejection sampling
4 Transforms (Box-Muller)
CHAPTER 2 : Markov Chain Monte Carlo Methods
1 On Markov Chains
2 Gibbs sampling
3 Other methods
CHAPTER 3 : Testing
1 On probability distances
2 Likelihood-based methods
3 Non likelihood based methods
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, ...)
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)
Recommended or required readings
All information (course notes, project and exercise sheets) will be made available via the eCampus platform.
- An Introduction to Statistical Learning with Applications in Rby Gareth James, Daniela Witten, Trevor Hastie, and Robert Tibshirani
- The Elements of Statistical Learningby Trevor Hastie, Robert Tibshirani, and David Friedman
- Monte Carlo methods in financial engineering by Paul Glasserman
- Diaconis, P. (2009). The Markov chain Monte Carlo revolution, Bulletin of the American Mathematical Society 46(2): 179-205.
- Dellaportas, P. and Roberts, G. O. (2003). An introduction to MCMC, Spatial statistics and computational methods, Springer New York, pp. 1-41.
- Fan, Y., Stephen P. Brooks, and Andrew Gelman. Output assessment for Monte Carlo simulations via the score statistic. Journal of Computational and Graphical Statistics1 (2006): 178-206.
Assessment methods and criteria
To be determined in terms of the project. Precise information will be communicated at the beginning of the course.
Office : B37 0/68 Phone : +32 4 366 94 76 Email : yswan at ulg.ac.be