Introduction to the Bayesian approach to statistics: Decision theory, prior distributions, hierarchical Bayes models, Bayesian tests and model selection, empirical Bayes, computational methods, Laplace approximation, Monte Carlo and Markov chain Monte Carlo methods.
August 25th 2017:
Beginning of lecture: Tuesday, 19/09/2017.
- Organization sheet
- Lecture Notes
|1||19/09||Interpretations of probability, Bayes formula, basics of Bayesian statistics|
|2||26/09||Point estimation and decision theory, testing, Bayes factor|
|3||03/10||Credible sets, Bayesian asymptotics, likelihood principle|
|4||10/10||Conjugate priors, Jeffreys prior and examples|
|5||17/10||Reference prior, expert priors, priors as regularizers|
|6||24/10||Hierarchical Bayes models and examples|
|7||31/10||Empirical Bayes and examples|
|8||07/11||Bayesian linear regression model and model selection|
|9||14/11||Laplace approximation, independent Monte Carlo methods|
|10||21/11||Rejection sampling, importance sampling, Basics of Markov chain Monte Carlo|
|11||28/11||MCMC, Gibbs sampler, Metropolis-Hastings algorithm|
|12||05/12||Adaptive MCMC, Hamiltonian Monte Carlo|
|13||12/12||Sequential Monte Carlo, approximate Bayesian computation|
|14||19/12||reserve / buffer|
Series and solutions
Submitting solutions to the exercise is not compulsory except for some PhD students. You can hand in your solution in the corresponding tray in HG J68.
|26/09||Posterior predictive distribution, Bayesian decision theory, Bayesian testing, Bayes factor||Series 1||Solution||03/10|
|10/10||Credible intervals, conjugate priors, improper priors||Series 2||Solution||17/10|
|24/10||Jeffreys prior and expert priors||Series 3||Solution||31/10|
|07/11||Empirical Bayes, Bayesian regression model||Series 4||Solution||14/11|
|28/11||MCMC: Gibbs sampler, random walk Metropolis algorithm||Series 5||Solution||05/12|
|12/12||Hamiltonian Monte Carlo||Series 6||Solution||19/12|
- Christian Robert, The Bayesian Choice, 2nd edition, Springer 2007.
- A. Gelman et al., Bayesian Data Analysis, 3rd edition, Chapman & Hall (2013).