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- Probabilty theory as an extension of Logic
2- Parameter estimation (without tears)
3- Model Selection
4- Representation of prior information
5- Bayesian decision theory
Course notes, supplied in digital form.
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