Aims

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.

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.

Content and teaching methods

- 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.

Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)

References :
Congdon, P. (2001) Bayesian Statistical Modelling. Wiley.
Gelman, A., Carlin, J.B., Stern, H.S. and Rubin, D.B. (1995) Bayesian Data Analysis. Chapman and Hall.
Robert, C.P. (1992) L'Analyse Statistique Bayesienne. Paris: Economica.
Robert, C.P. (1994) The Bayesian Choice. New York: Springer-Verlag.
Spiegelhalter, D.J., Thomas, A. and Best, N.G. (1999) WinBUGS User Manual. MRC Biostatistics Unit.

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