| Date |
Lesson
topics |
| 20/5/2013 |
The
meaning of mathematical and empirical probabilities.
Bayes' theorem. Discussion of frequentist and Bayesian
standpoints (links to papers by F.James,
M.
Goldstein and D.
Cox). Examples and applications of Bayes' theorem
(medical tests, etc.) (link to
slides). |
| 21/5/2013 |
Shall the sun rise tomorrow (Laplace). Bayesian inference, discrete hypotheses, parameter inference. Bayes factors. Exercise to demonstrate both discrete and continuous parameter tests, marginalization of nuisance parameters, and Bayes factors. Examples of Bayesian inference: 1. parameter of a binomial model (and Beta pdf posterior); 2. parameter of a Poisson model (and Gamma pdf posterior); 3. mean value of a Gaussian model (and Gaussian pdf posterior). Link with Max. Likelihood formalism. (link to slides). |
| 22/5/2013 |
More on the connection between Bayes' theorem, MLE formalism and least squares. Prior distributions. Priors from symmetry arguments. Maximum Entropy Method (MEM). The kangaroo problem. Priors from MEM. (link to slides). |
| 23/6/2013 |
A few
examples of Bayesian techniques: 1. straight-line fit; 2.
weighted mean; 3. systematic errors; 4. a two-dimensional
location problem; 5. search for weak signals in
spectra. (link to slides).
|
| 3/6/2013 |
Applications of Bayesian reasoning: 1. the EM algorithm; 2. image processing algorithms (link to slides). |
| 4/6/2013 |
Image
processing algorithms (ctd.). Numerical evaluation methods and Bayesian statistics. Acceptance-rejection sampling; importance sampling; statistical bootstrap; Bayesian methods in a sampling-resampling perspective; introduction to Markov chains and to the Metropolis algorithm. (link to slides). |
| 5/6/2013 |
Bayesian methods in a sampling-resampling perspective (ctd.). The Markov Chain Monte Carlo (MCMC) method. Bayesian learning. Naive Bayesian classifiers. Differences between Bayesian learning and MEM learning. The AUTOCLASS unsupervised Bayesian classifier. (link to slides). |
| date TBD |
Exams
(talks given by students). |