# 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

12080

6.0

##### Responsible teacher

Miguel dos Santos Fonseca

Weekly - 4

Total - 68

Português

Available soon

### Bibliography

Main:

- 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).

- Bernardo J.M. & Smith, A.F.M. (1994). Bayesian theory. Wiley.

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

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

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

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

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

- Turkman, M., Paulino, C., Müller, P. (2019). Computational Bayesian Statistics, Cambridge.

### 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 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

## Programs

Programs where the course is taught: