2017-2018 / MATH2022-1

Large sample analysis : theory and practice

Duration

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 

Lecturer

N..., Yvik Swan

Coordinator

Yvik Swan

Language(s) of instruction

English language

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 Metropolis-Hastings
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, ...)
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)

face-to-face

Recommended or required readings

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


  • 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
Articles:


  • 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.

Work placement(s)

Organizational remarks

Contacts

Yvik Swan 
Office : B37 0/68 Phone : +32 4 366 94 76 Email : yswan at  ulg.ac.be