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6340 Bayesian Inference - Three-year degree in Statistical Sciences and Techniques

Center

Faculty of Mathematics

Departament

Statistics and Operational Research

Lecturers in charge

Sin datos cargados

Met. Docent

Met. Avaluació

Final examination - -

Bibliografia

Bibliografía básica
(1) Berger, J. O. (1985). Statistical Decision Theory and Bayesian Analysis (2nd. ed). Springer-Verlag.
(2) Gelman, A., Carlin, J. B., Stern, H. and Rubin, D.B. (1995). Bayesian Data Analysis. Chapman and Hall.
(3) Lee, P. M. (1989). Bayesian Statistics: An Introduction (2nd. ed). Arnold.
Bibliografía complementaria
(1) Carlin, B.P. y Louis, T.A. (1996). Bayes and Empirical Bayes Methods for data Analysis. Chapman and Hall.
(2) O'Hagan, A. (1994). Kendall's Advance Theory of Statistics, Vol. 2B: BayesianInference. John Wiley and Sons Inc.

Continguts

Goals
To provide students with a global overview of Bayesian paradigm. To describe its foundations and simple methodological tools; In particular, emphasize objective Bayesian methods. To provide students with the needed tools to solve not too complex inferential tasks from a Bayesian point of view.

Theory programme
1 Preliminaries. Foundations.2 Modeling. The learning process.3 Inference. Point and interval estimation.4 Multivariate parameters.5. Analytical and numerical approximations.5 Hypothesis testing and Model selection.

Practical programme
Students will solve problems and fully address simple case studies, requiring both analytical and numerical solutions, with the aid of some statistical package (mainly R, maybe some First Bayes). The next main themes will be addressed (not necessarily in this order):
1 Quantification of informative priors, Computation of objective priors.
2 Basic concepts in the learning process. Usual Fallacies.
3 Single-parameter models.
4 Multiparameter models.
5 Simulation based inference.

Objetius

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