8231 - BAYESIAN STATISTICAL METHODS
MM-LS - AFC-LS - CLAPI-LS - CLEFIN-LS - CLELI-LS - DES-LS - CLG-LS - M-LS - IM-LS - ACME-LS - EMIT-LS
Course taught in English
Go to class group/s: 31
The course is intended to be an introduction to Bayesian statistics for students who have already been exposed to a good preliminary course of statistics from a classical point of view.
We also assume that our audience includes those who are interested in using Bayesian methods to model real problems in various scientific disciplines (economics, finance, econometrics, survival analysis, demography, reliability, etc.)
Such students usually want to understand foundational principles well enough so that they feel comfortable using statistical procedures; are able to recommend solutions based upon these procedures to decision makers; are intrigued enough to seek additional background understanding through relevant literature.
For this reason we have tried to maximize interpretation of the theory and have minimized our dependence upon proof of theorems.
Definition of coherence; definition of probability; existence of a probability; properties.
The Bayesian Methods
Bayes' Theorem; Posterior Distributions; Prior Distributions; Decision Theory.
Predictive and parametric inference; Coniugate Analysis; Parametric point estimation; Test of Hypotheses.
Exchangeable sequences of random variables
Exchangeability events; mixtures of i.i.d. random variables and exchangeability; de Finetti's representation theorem; partial exchangeability according to de Finetti; partial exchangeability according to Diaconis and Freedman.
Predictive sufficient statistics
Predictive sufficient statistic: definitions and properties; connections between predictive sufficient statistics and statistical models; predictive sufficient statistics and exchangeability; exchangeability and characterizations of the models; predictive justifications of the priors.
Prior processes for the Bayesian non-parametric
Constructing random probability measures; the Dirichlet process; polya Trees; neutral to the right priors.
Urn schemes for constructing priors
Background on two colors urn processes; a Polya urn for the Dirichlet process; reinforced urn processes; reinforced urn processes for the beta-Stacy prior; reinforced urn processes for the Polya tree; neutral to the prior;
Linear models; Kalman filter.
The exam consists of an essay on a topic chosen by the student, that is discussed with the professors.
- M.J. BERNARDO , A.F.M. SMITH, Bayesian Theory, J. Wiley, 1994.