# BAYES

Bayesian Statistical Modeling
This curricular unit aims to foster the necessary knowledge and skills that may allow students to understand, interprete and apply Bayesian inference methods, as a complement or alternative to the classical frequentist statistics, and classification and prediction methods using Bayesian Networks, to explore associations between factors and outcomes and for medical decision support.
At the end of this unit the students are expected to adequately apply and interprete Bayesian inference methods, in the context of basic and common statistical inference problems; and Bayesian Networks, in the context of classification and prediction problems and medical decision support. Students should also be able to adequately use, in order to solve basic problems and exercices, specific software for Bayesian inference (OpenBugs and R2OpenBugs) and Bayesian Networks (R and Samiam).
Bayesian Inference:
– Introduction to Bayesian inference: Probability and parameters; Classical frequentist inference versus Bayesian inference; Foundations of the Bayesian inference; Prior distributions; Posterior distributions; Posterior predictive distributions; Basic Bayesian models; Bayesian hierarchical models; Models building and evaluation.
– Building Bayesian inference models: Bayesian inference with conjugate priors; Bayesian computation – Monte Carlo methods, Markov Chains Monte Carlo methods (MCMC), Metropolis-Hastings algorithm, Gibbs sampler and other related algorithms; Assessment of the quality of the models (choosing initial values, convergence, efficiency and accuracy); Methods for model selection; Applying Bayesian methods in common inference problems – regression models, categorical data analysis, models for evidence synthesis.
Bayesian Networks:
– Introduction to Bayesian networks: Motivation and examples; Probability and medical applications; Probabilistic graphical models; Semantics and factorization in Bayesian networks.
– Building Bayesian networks from data: Machine learning; Bayesian network parameter estimation; Bayesian network structure learning; Learning and inferring from incomplete data.
The syllabus will enable students to acquire the necessary and sufficient concepts and skills to understand and apply modern methods of statistical analysis and probability to solve biomedical problems and specifically to apply the theory and practice of Bayesian inference and Bayesian Networks.
Theoretical lectures and practical lessons, with topic discussion, individual and group exercises, and hands-on training with specific software. Evaluation will be based on practical assignments (30%) and final exam (70%).
The theoretical exposition allows to transmit to students the concepts that allow them to describe, identify and characterize aspects related to the theory and practice of Bayesian inference and Bayesian Networks. The group discussions and the individual and group assignments, using specific software, enables students to develop skills that allow them to integrate these new methods in their daily research practice.
Lunn D, Jackson C, Best N, Thomas A, Spiegelhalter D. The BUGS book: A practical introduction to Bayesian analysis. CRC press, 2012.
Carlin BP, & Louis TA. Bayesian methods for data analysis. CRC Press, 2008.
Welton NJ, Sutton AJ, Cooper N, Abrahams JR & Ades AE. Evidence synthesis for decision making in healthcare. John Wiley & Sons, 2012.
Paulino, D., Amaral Turkman, M.A., Murteira, B. E Faria, J.F. (2003) Estatística Bayesiana, Fundação Calouste Gulbenkian, Lisboa
Darwiche, A. (2009). Modeling and Reasoning with Bayesian Networks. Cambridge University Press.
Darwiche, A. (2010). Bayesian networks. Communications of the ACM, 53(12), 80–90.
Lucas, P. J. F., van der Gaag, L. C., & Abu-Hanna, A. (2004). Bayesian networks in biomedicine and health-care. Artificial Intelligence in Medicine, 30(3), 201–14.
Lucas, P. (2004). Bayesian analysis, pattern analysis, and data mining in health care. Current Opinion in Critical Care, 10(5), 399–403.
Koller, D., & Friedman, N. (2009). Probabilistic Graphical Models – Principles and Techniques. MIT Press.
Cowell, R. G., Dawid, P., Lauritzen, S. L., & Spiegelhalter, D. J. (2007). Probabilistic Networks and Expert Systems: Exact Computational Methods for Bayesian Networks. Springer.