Introduction to Bayesian statistics

Teacher(s)

Lambert Philippe;

Language

English

Main themes

- The Bayesian model: basic principles. - The likelihood function and its a priori specification. - One-parameter models: choice of the a priori distribution, derivation of the a posteriori distribution, summarizing the a posteriori distribution. - Multi-parameter models: choice of the a priori distribution, derivation of the a posteriori distribution, nuisance parameters. Special cases: the multinomial and the multivariate Gaussian models. - Large sample inference and connections with asymptotic frequentist inference. - Bayesian computation.

Aims

At the end of this learning unit, the student is able to :
1	By the end of the course, the student will be familiar with the principles and the basic techniques in Bayesian statistics. He or she will be able to use and to put forward the advantages and drawbacks of that paradigm in standard problems.

Content

- The Bayesian model: basic principles. - The likelihood function and its a priori specification. - One-parameter models: choice of the a priori distribution, derivation of the a posteriori distribution, summarizing the a posteriori distribution. - Multi-parameter models: choice of the a priori distribution, derivation of the a posteriori distribution, nuisance parameters. Special cases: the multinomial and the multivariate Gaussian models. - Large sample inference and connections with asymptotic frequentist inference. - Bayesian computation.

Bibliography

Gelman, A., Carlin, J.B., Stern, H.S. and Rubin, D.B. (2003,2nd edition) Bayesian Data Analysis. Chapman and Hall.
Spiegelhalter, D.J., Thomas, A. and Best, N.G. (1999) WinBUGS User Manual. MRC Biostatistics Unit.
Bolstad, W.M.(2004) Introduction to Bayesian Statistics. Wiley.

Faculty or entity

LSBA