Phd Course in Mathematical and Physical Sciences

2022-2023

Advanced Bayesian Statistics

Advanced Course

Lecturer

Alessandra Rosalba Brazzale, Andrea Sottosanti
University of Padova
Board Contact
Michela Battauz, Valentina Mameli
SSD
SECS-S/01
CFU
3+2
Period
June/July 2023
Lessons / Hours
4 lectures of 3 hours each
Program
Each lacture consists of an introductory theoretical part followed by practical exercises in R

1. Bayes’ theorem
T: Introduction, likelihood principle, posterior summaries
E: Conjugacy, Laplace approximation, numerical integration
2. Bayesian computation via Markov chain Monte Carlo
T: Importance sampling, Gibbs sampler, Metropolis-Hastings algorithm)
E: Data augmentation
3. Output analysis
T: Multiple chains, convergence diagnostics (autocorrelation, potential scale reduction, effective sample size)
E: How to set an MCMC sampler
4. Approximate Bayesian computation
T: Distance functions, summary functions, pitfalls and remedies
E: Model comparison and model choice
Verification
Final assignment
Prerequisites
Knowledge of R; basic notions of statistical inference based on the likelihood function