Introduction to Bayesian Probability and Statistics
Cod: 21073
Department: DCET
ECTS: 6
Scientific area: Mathematics
Total working hours: 156
Total contact time: 26

In this curricular unit we present Bayesian theory as framework in which to answer the question: how can one think and decide rationally under the weight of uncertainty.

Classical logic tells us how to infer the truth of some propositions from other propositions whose truth value is known. This situation, alas, almost never happens in the real world.

In this unit we present the basic concepts of the Bayesian theory of Probability as the single extension of classical Logic to the space of propositions of unknown logical value. We show how probability is the extension of truth value, and how the rules of logical inference can be generalized. We also present the basic concepts of Bayesian decision theory, and briefly reference current real-world applications.

1. Bayes
2. Probability
3. Logic
4. Statistics

The student is expected to learn the basic techniques and concepts of Bayesian probability and decision theory. The student will learn how to apply these techniques to real world problems, how to decide on a prior, how to model a problem, and how to infer conclusions and reach decisions based on the concepts presented.

1- Probabilty theory as an extension of Logic
2- Parameter estimation (without tears)
3- Model Selection
4- Representation of prior information
5- Bayesian decision theory
6- Applications

Mandatory:
Course notes, supplied in digital form.
Complementary:
1- B. Murteira: Estatística Bayesiana, Fundação Calouste Gulbenkian, Lisboa, 2003
2- D. S. Sivia: Data Analysis – A Bayesian Tutorial, Oxford University Press, 1996 

3- E.T. Jaynes: Probability theory: the logic of science, Cambridge University Press, 2003

E-learning.

Continuous assessment is privileged: 2 or 3 digital written documents (e-folios) during the semester (40%) and a presence-based final exam (p-folio) in the end of the semester (60%). In due time, students can alternatively choose to perform one final presence-based exam (100%).

Students are recommended to have previously knowledge in the Linear Algebra I curricular unit as well as either in the Elements of Infinitesimal Analysis I curricular unit or in the Calculus for Computer Science curricular unit.