Bayesian Analysis
A.Y. 2023/2024
Learning objectives
The aim of the course is to introduce the Bayesian approach to statistical inference. The course will develop the relevant methodology, theory and computational techniques necessary to its implementation. In the course single and multi-parameter models as well as the fundamental of Bayesian regression analysis will be discussed. Monte Carlo summaries of posterior distributions will be shown through the use of Gibbs sampler and Metropolis Hastings techniques.
Expected learning outcomes
At the end of the course, the students will be able to deal with the Bayesian inference. In particular, the students will understand how the Bayesian inference works for single and multiple parameters. As a further step, the students will improve their computational and methodologial skills through the use of R software for Bayesian modeling.
Lesson period: Second trimester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
Second trimester
Course syllabus
The course will cover the following topics:
-) Recall of probability and exchangeability
-) General idea of Bayesian analysis (including Bayes theorem for distributions)
-) Prior and posterior distributions (conjugate priors)
-) Different levels of prior knowledge; asymptotic posterior distribution
-) Bayesian inference (point estimates and intervals estimates) and prediction
-) Inference for the normal distribution
-) Asymptotic posterior for the multiparameter case
-) Rejection and Importance sampling techniques
-) Markov Chain Monte Carlo (MCMC) and Metropolis-Hastings (MH) techniques for non-conjugate analysis
-) Convergence and Diagnostic Analysis (CODA)
-) Applications to real data (time series and regressions)
-) Recall of probability and exchangeability
-) General idea of Bayesian analysis (including Bayes theorem for distributions)
-) Prior and posterior distributions (conjugate priors)
-) Different levels of prior knowledge; asymptotic posterior distribution
-) Bayesian inference (point estimates and intervals estimates) and prediction
-) Inference for the normal distribution
-) Asymptotic posterior for the multiparameter case
-) Rejection and Importance sampling techniques
-) Markov Chain Monte Carlo (MCMC) and Metropolis-Hastings (MH) techniques for non-conjugate analysis
-) Convergence and Diagnostic Analysis (CODA)
-) Applications to real data (time series and regressions)
Prerequisites for admission
Good basis of mathematics (differentiation, integration). Good knowledge of classical statistics (random variables, probability, central limit theorem, point and interval estimation).
Teaching methods
Teaching will mainly be delivered through lectures and practical (in R and Matlab) classes.
Teaching Resources
-) Lectures Notes;
-) "A First Course in Bayesian Statistical Methods" by Peter D. Hoff (editor Springer)
-) "Bayesian Data Analysis" by Gelman, Carlin, Stern, Dunson, Vehtari, Rubin (editor
Routledge)
-) "Bayesian Econometric Methods" by J. Chan, G. Koop, D. Poirier and J. Tobias (editor Cambridge)
-) "The Bayesian Choice" by C. P. Robert (editor Springer)
-) "Bayesian Core: A Practical Approach to Computational Bayesian Statistics" by J. M.
Marin and C. P. Robert (editor Springer).
-) "Introducing Monte Carlo Methods with R by C. P. Robert and G. Casella (editor
Springer).
-) "A First Course in Bayesian Statistical Methods" by Peter D. Hoff (editor Springer)
-) "Bayesian Data Analysis" by Gelman, Carlin, Stern, Dunson, Vehtari, Rubin (editor
Routledge)
-) "Bayesian Econometric Methods" by J. Chan, G. Koop, D. Poirier and J. Tobias (editor Cambridge)
-) "The Bayesian Choice" by C. P. Robert (editor Springer)
-) "Bayesian Core: A Practical Approach to Computational Bayesian Statistics" by J. M.
Marin and C. P. Robert (editor Springer).
-) "Introducing Monte Carlo Methods with R by C. P. Robert and G. Casella (editor
Springer).
Assessment methods and Criteria
Short Project (maximum 15 pages) and its presentation.
Educational website(s)
Professor(s)
Reception:
Each Wednesday 12-14
DEMM, room 31, 3° floor (By appointment, please send an email)