Advanced Course
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Lecturers:
Alessandra Rosalba Brazzale, Andrea Sottosanti (University of Padova)
Board Contact:
Michela Battauz, Valentina Mameli
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SSD: SECS-S/01
CFU: 3+2
Period: June/July 2023
Lessons / Hours: 4 lectures of 3 hours each
Program:
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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
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Verification: Final assignment
Prerequisites: Knowledge of R; basic notions of statistical inference based on the likelihood function