| Date |
Topics |
Useful links |
| 3/6/2014 |
The meaning of mathematical and empirical
probabilities. The physics of coin tossing. Bertrand's
paradox and equiprobable events. Probabilities as measures
of "reasonable expectation" (R. T. Cox, link to paper here). The algebra
of probabilities and 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). |
|
| 3/6/2014 |
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 to slides). | |
| 4/6/2014 |
Link with Maximum Likelihood (ML) formalism and least squares. Prior distributions. Priors from symmetry arguments. Boltzmann entropy and Shannon entropy. Maximum Entropy Method (MEM). The kangaroo problem. The Kullback-Leibler divergence. Priors from MEM. (link to slides). | |
| 4/6/2014 |
Priors from MEM (ctd.). 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). |
|
| 5/6/2014 |
Algorithmic applications of Bayesian methods: 1. the EM algorithm; 2. image processing algorithms (link to slides). | |
| 5/6/2014 |
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). | |
| 6/6/2014 |
Introduction to
Markov chains and to the Metropolis algorithm. (ctd.) 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 |
Students'
talks |