Παρουσίαση/Προβολή

(STAT219) -  Panagiotis Tsiamyrtzis

Περιγραφή Μαθήματος

Syllabus:

Introduction to the Bayesian Philosophy: The three schools of thought in Statistics, Fiducial – Frequentist – Bayesian will be presented. We will provide the framework of subjective probability and use the Bayes theorem, as an updating mechanism of prior to posterior distribution.

Prior distributions: prior elicitation, conjugate, non-informative, improper, Jeffreys prior, mixtures and hyperpriors. Sensitivity analysis. Empirical Bayes approach. Sequential updating of the posterior distribution.

Topics in multivariate Bayesian analysis and hierarchical modeling

Bayesian Inference from a Decision Theory perspective: Basic elements of decision theory. Loss function, frequentist, posterior and Bayes risk. Bayes and minimax rule. Bayesian inference (point/interval estimation and hypothesis testing) from a Bayesian perspective: Bayes rules, credible sets, Highest Posterior Density sets, Bayes factor and Bayes test.

Predictive Inference

Bayesian Asymptotic Methods: Bayesian central limit theorem and Laplace’s method.

MCMC algorithms for the estimation of the posterior distributions: Gibbs sampling and Metropolis Hastings.

Recommended Bibliography

Carlin B. and Louis T. (2008), Bayes and Empirical Bayes Methods for Data Analysis. 3rd Edition, London: Chapman and Hall.

Ntzoufras, I. (2009). Bayesian Modeling Using WinBUGS. Wiley. Hoboken. USA.

Ημερομηνία δημιουργίας

Τρίτη, 21 Φεβρουαρίου 2017