Bayesian statistics

Duration

30h Th, 10h Pr, 20h Mon. WS

Number of credits

Lecturer

Philippe Lambert

Language(s) of instruction

French 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

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

Practicals will be organized to illustrate the concepts and techniques studied during the theoretical course. Some exercises will require the use of the R software and possibly of a more specialized software like JAGS or WinBUGS.

Mode of delivery (face-to-face ; distance-learning)

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 used during the course will be made available with the associated list of references.

Assessment methods and criteria

The assessement is made during a written exam. Part of the final grade is based on a written report deposited by each student before the end of the 2nd quadrimester. A student won't be allowed to take the exam if he/she did not transmit the above mentioned written report at the prescribed time and in the required format.

Work placement(s)

Organizational remarks

Attending the theoretical lectures is compulsory: it is a necessary condition to access the practicals.

Contacts

Philippe LAMBERT, Institut des sciences humaines et sociales, Bât B31, local R.54, tél: 04/366.59.90, email: p.lambert@uliege.be

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