Statistique bayésienne
UE-EIG.00027
Teacher(s): Donzé Laurent |
Level: Master |
Type of lesson: Lecture |
ECTS: 4.5 |
Language(s): French |
Semester(s): SS-2024 |
The course is an introduction to Bayesian Statistics:
- Bayesian inference (Introduction; Bayesian inference for discrete random variables; Bayesian inference for the proportion pi of a binomial distribution; Bayesian inference for the mean of the normal distribution; Bayesian inference for the standard deviation of a normal distribution)
- Simulation of posterior distributions (Importance sampling; Markov Chains Monte Carlo (MCMC); Gibbs algorithm; Metropolis-Hastings algorithm; calculation of marginal likelihood; numerical standard errors; convergence diagnostic)
- Regression models and specific models (Linear regression model; hierarchical model; selection of Bayesian models; MCMC for regression models)
The theoretical concepts and methods are illustrated by practical applications. R is the software used.
Training aims
The course is part of the supplied of Master courses in applied statistics, which is a packet of four half-yearly ones of 4.5 ECTS (one by semester) over two years:
- Topics in multivariate statistics
- Introduction to Bayesian statistics
- Inference, evaluation, and selection of models
- Classification methods
Although they complete each other, they can be chosen separately. Of general interest, the set of courses gives a broad view of problems and applied statistical methods, and of the data science. A server of Jupyter notebooks completes the course.
There is no specific public. Although the courses are primarily conceived for students of the Faculty of Management, Economics and Social Sciences, they can be attended by other students.
The student will benefit not only of theoretical knowledge but is also skilled in the use of the methods presented during the course.
Documentation
A script with a listing of references is provided. The student will find on the course's Moodle platform other resources.
- ALBERT, Jim (2007). Bayesian Computation with R. Springer.
- BOLSTAD, William M. (2007). Introduction to Bayesian Statistics. John Wiley & Sons, Inc.
- GELMAN, Andrew et al. (2004). Bayesian Data Analysis. Chapman & Hall/CRC.
- GHOSH, Jayanta K., Mohan DELAMPADY et Tapas SAMANTA (2006). An Introduction to Bayesian Analysis. Theory and Methods. Springer.
- GREENBERG, Edward (2008). Introduction to Bayesian Econometrics. Cambridge Uni[1]versity Press.
- HOFF, Peter D. (2009). A First Course in Bayesian Statistical Methods. Springer Texts in Statistics. Springer. 270 p. ISBN : 978-0-387-92299-7. DOI : 10.1007/978-0-38 7-92407-6.
- KRUSCHKE, John K. (2015). Doing Bayesian Data Analysis. Second edition. Elsevier. ISBN : 978-0-12-405888-0.
- LEONARD, Thomas et John S. J. HSU (1999). Bayesian Methods. An Analysis for Statisticians and Interdisciplinary Researchers. Cambridge University Press.
- VALLVERDÚ, Jordi (2016). Bayesian Versus Frequentists. A Philosophical Debate on Statistical Reasoning. Springer Briefs in Statistics. Springer. 110 p. ISBN : 978-3- 662-48636-8. DOI : 10.1007/978-3-662-48638-2.