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Bayesian Methods

Objectives

The Bayesian paradigm is an important option in statistics by its flexibility in handling complex problems and its corresponding easiness of common interpretation of statistical conclusions. Its use has been potentiated by the huge computational development. The main objective of this CU is to introduce the Bayesian statistics approach. By the end of this CU, a student must understand the principles that rules Bayesian inference, know how to incorporate, in various problems, the existing prior knowledge and its corresponding uncertainty in a probability distribution, know how to update the prior distribution with data to estimate analytically or numerically the resulting posterior probability distribution, through intensive programming methods as Markov Chain Monte Carlo (MCMC) and  know how to use hierarchical modelling to represent and analyze complex systems, using the software R-project and BUGS (run in R).

General characterization

Code

12080

Credits

6.0

Responsible teacher

Isabel Cristina Maciel Natário

Hours

Weekly - 4

Total - 68

Teaching language

Português

Prerequisites

Available soon

Bibliography

Main:

- Paulino, C. & Turkman, M.A. Estatística Bayesiana Computacional - uma introdução, 2ª edição. (Edições SPE, 2020). 

- Johnson, A. A., Ott, M. Q. & Dogucu, M. Bayes Rules!, An Introduction to Applied Bayesian Modeling. (Chapman & Hall, 2022).

- Kruschke, J. K. Doing Bayesian data analysis: a tutorial with R, JAGS, and Stan. (Academic Press, 2015).

 

Additional:

- Albert, J. Bayesian Computation with R. (Springer, 2009).

- Congdon P. Bayesian Statistical Modelling. (Wiley, 2001).

- Gelman, A., Carlin, J.B., Stern, H.S., Rubin, D.B. Bayesian Data Analysis, 2nd edition. (Chapman and Hall / CRC, 2003).

- Lee, P.M. Bayesian Statistics: An Introduction, 3rd edition. (Arnold, 2004).

- Paulino, C., Turkman, M.A., Murteira, B., Silva, G. Estatística Bayesiana. (Gulbenkian, 2018).

- Reich, B. J. & Ghosh, S. K. Bayesian Statistical Methods. (2019).

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 3 moments:

Individual assignment, mini-test (10% of the grade)

Individual assignment, test (50% of the grade)

Final assigment (40% of grade)

There is a minimum grade in the test (8/20) and in the assigment (8/20). The final grade must be >= 9.5/20.

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