B030005 - BAYESIAN STATISTICS

Italian

Stochastic processes; Historical and philosofical introduction to Bayesian statistics; Parametric inference and main exact Bayesian computations (one-parameter models); Conjugate priors; Non-informative priors; Computational methods (Monte Carlo and Markov Chain Monte Carlo); Normal model; Multivariate Normal model; Hierarchical model.

Peter D. Hoff A First Course in Bayesian Statistical Methods, 2009 Springer

KNOWLEDGE AND COMPREHENSION:
This course intends to equip students with insightful knowledge of the basic Bayesian inference notions. Aim of this course is to introduce parametric models where the parameters are treated as random variables and to comprehend the challenges related to the inferential procedures on such models.

ABILITY TO APPLY KNOWLEDGE AND COMPREHENSION:
Students will be able to frame and handle inferential procedures on univariate and multivariate models with hierarchical structure using a Bayesian approach

COMMUNICATIVE SKILLS:
Students will develop the necessary skills to communicate and interpret the results of a Bayesian data analysis

Statistical inference and computational methods.
Background knowledge of the R software is needed.

Oral lectures and sessions of exercises.

---

Grading of the homeworks provided during the class and written test

In the written test it will be evaluated the acquired knowledge on the fundamental principles of Bayesian inference, Bayesian modeling, estimation and predicion methods, and on the challenges posed by Bayesian inference.

Finally it will be evaluated the way results are presented and the critical ability developed during the weekly homework assignments.

Stochastic processes
Exchangeability and De Finetti's theorem
Bayes' rule and philosophical introduction to Bayesian statistics
Binomial model
Poisson Model
Exponential family and conjugate prior distributions
Non-informative prior distributions
Introduction to Monte Carlo methods
Acceptance-Rejection algorithm
Importance Sampling
Markov chains and introduction to Markov Chain Monte Carlo methods
Gibbs Sampling
Metropolis algorithm
Metropolis-Hastings algorithm
Normal model
Multivariate Normal model
Hierarchical modeling
Introduction to model checking and missing data imputation
Introduction to linear regression

N.A.