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.
September 3rd 2021:
Beginning of lecture: Tuesday, 21/09/2021.
All the course materials can be found on the Moodle webpage. An overview is given below.
|1||21/09||Introduction, Bayes formula, basics of Bayesian statistics, interpretations of probability
|2||28/09||Point estimation and decision theory, testing, Bayes factor
|3||05/10||Credible sets, Bayesian asymptotics, likelihood principle, conjugate priors
|4||12/10||Non-informative priors, improper priors, Jeffreys prior
|5||19/10||Reference prior, expert priors, priors as regularizers
|6||26/10||Hierarchical Bayes models
|8||09/11||Bayesian linear regression model & model selection
|9||16/11||Laplace approximation, independent Monte Carlo methods
|10||23/11||Rejection sampling, importance sampling, Basics of Markov chain Monte Carlo
|11||30/11||MCMC, Gibbs sampler, Metropolis-Hastings algorithm
|12||07/12||Adaptive MCMC, Hamiltonian Monte Carlo
|13||14/12||Sequential Monte Carlo, approximate Bayesian computation
Series and solutions
Submitting solutions to the exercises is not compulsory except for some PhD students. You can hand in your solutions by email to Drago Plecko.
|28/09||Posterior predictive distribution, Bayesian decision theory, Bayesian testing, Bayes factor||Series 1||Solutions 1||05/10|
|12/10||Credible intervals, conjugate priors, improper priors||Series 2||Solution 2||19/10|
|26/10||Jeffreys prior, reference prior, expert priors||Series 3||Solution 3||02/11|
|09/11||Empirical Bayes, Bayesian regression model||Series 4||Solution 4||16/11|
|30/11||MCMC: Gibbs sampler, random walk Metropolis algorithm||Series 5||Solution 5||07/12|
|14/12||Hamiltonian Monte Carlo||Series 6||Solution 6||21/12|
- Christian Robert, The Bayesian Choice, 2nd edition, Springer 2007.
- A. Gelman et al., Bayesian Data Analysis, 3rd edition, Chapman & Hall (2013).