Duration
30h Th, 10h Pr, 20h Mon. WS
Number of credits
| Master in mathematics (120 ECTS) (Even years, not organized in 2023-2024) | 8 crédits |
Lecturer
Language(s) of instruction
French language
Organisation and examination
Teaching in the second semester
Schedule
Units courses prerequisite and corequisite
Prerequisite or corequisite units are presented within each program
Learning unit contents
CAREFUL: the course is only organized during the even academic years (2022-2023, 2024-2025).
This course is an introduction to Bayesian statistics.
After defining subjective probabilities, the basic principles underlying Bayesian inference are presented through the estimation of a proportion.
The same principles are used to compare proportions and rates. The estimation of a mean (variance) in a normal distribution is also studied when the variance (mean) is unknown.
Inference in multiparameter models is also tackled. The concepts of marginal and conditional posterior distributions, credible regions and predictive distributions are defined. It is first illustrated with the joint estimation of the mean and of the variance of a normal distribution. The comparison of two means of a normal distribution with known or unknown variance(s) is also tackled. A solution is obtained with the simulation of a random sample from the joint posterior distribution when the variances cannot be assumed equal. The multiple regression model and the ANOVA I model are also studied in a Bayesian framework.
The basic algorithms enabling to generate a random sample from the posterior distribution are presented as these are fundamental to make inference in complex models.
The course is concluded with a short introduction to hierarchical models.
Learning outcomes of the learning unit
The goals of the course are: - To present the basic principles and techniques in Bayesian statistics. - To show that problems tackled in an ad-hoc way in a frequentist setting can be solved systematically in a Bayesian framework. - To understand and to be able to use Monte Carlo algorithms to sample from a joint posterior. - To show how problems difficult to tackle in a frequentist setting can be solved in a Bayesian framework.
Prerequisite knowledge and skills
It is assumed that students have a basic training in probability, in inference and in the use of the statistics software R.
Planned learning activities and teaching methods
Exercises to be solved without supervision will be proposed in order to illustrate the implementation of the techniques seen in the course. Some of them will require the use of the R software and possibly of a specialised software such as JAGS or WinBUGS.
Mode of delivery (face to face, distance learning, hybrid learning)
Blended learning
Additional information:
The course and the practicals are organized during the 2nd semester. It could take the form of a directed reading if the number of registered students is small.
Recommended or required readings
The slides (in English) and some podcasts (also in English) used during the course will be made available to the students, as well as the list of references used for their elaboration.
Exam(s) in session
Any session
- In-person
written exam ( open-ended questions )
Written work / report
Additional information:
The assessment of this course will combine a written exam (on 15 points) and a project (on 5 points). This project will take the form of a written report submitted by each student before the beginning of the 1st exam session, without the possibility to submit it later on. However, the mark obtained for this work will be used in the same way during the two sessions to calculate the final mark.
Work placement(s)
Organisational remarks and main changes to the course
Attending the theoretical lectures is compulsory.
CAREFUL: the course is only organized during the even academic years (2022-2023, 2024-2025).
Contacts
Philippe LAMBERT, Institut des sciences humaines et sociales, Bât B31, local R.54, tél: 04/366.59.90, email: p.lambert@uliege.be