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Bayesian Methods

Objectives

The objective of this curricular unit is to learn the Bayesian paradigm in the statistical analysis of data, methodologies and computational techniques for inference, hypothesis testing and prediction.

General characterization

Code

12080

Credits

6.0

Responsible teacher

Miguel dos Santos Fonseca

Hours

Weekly - 4

Total - 68

Teaching language

Inglês

Prerequisites

Available soon

Bibliography

1. Albert, J. (2009). Bayesian Computation with R. Spinger.
2. Bernardo J.M. & Smith, A.F.M. (1994). Bayesian theory. Wiley.
3. Congdon P (2001). Bayesian Statistical Modelling. Wiley.
4. Cowles, M.K. (2013). Applied Bayesian Statistics. With R and OpenBUGS Examples. Springer.
5. Gamerman, D. & Lopes, H.F. (2006). Markov chain Monte Carlo - stochastic simulation for Bayesian inference. 6. Chapman & Hall/CRC.
7. Gelman, A., Carlin, J.B., Stern, H.S., Rubin, D.B. (2003). Bayesian Data Analysis (2nd edition).
8. Chapman and Hall / CRC, 2003.
9. Gilks, W.R., Richardson, S. and Spiegelhalter, D. (Edts.) (1996) Markov chain Monte Carlo in Practice. Chapman and Hall/CRC.
10. Lee, P.M. (2004). Bayesian Statistics: An Introduction, 3rd edition, Arnold.
11. Turkman, M., Paulino, C., Müller, P. (2019). Computational Bayesian Statistics, Cambridge
12. Paulino, C., Turkman, M., Murteira, B., Silva, G. (2018). Estatística Bayesiana. Gulbenkian 

Teaching method

Lecture-lab classes are the adequate way to convey the course contents to students as, together with the explanation of the main concepts and results, illustrative examples are given. Afterwards, some problems are proposed to students to be solved in a lab, being students supposed to take active part in their resolution. Consequently, students acquire the basic expertise not only of the adequate implementation of the methodologies learned in each concrete situation but also of the application of the statistic software

Evaluation method

The evaluation will be done in 2 moments:

Individual assignment (50% of the grade) - TBA

Final individual work (50% of grade) -TBA

Subject matter

1 - The Bayesian paradigm
2 - The prior distribution and methods for its formulation
3 - The likelihood function, the posterior distribution, the marginal and predictive distributions
4 - Bayesian inference
5 - Markov Chain Monte Carlo, MCMC
6 - Model evaluation and selection
7 - Hierarchical models