Course description

This course is a basic introduction to Bayesian techniques, in the framework of the Physics PhD course of the Physics Department of the University of Trieste.

Course program

(grayed text means preliminary program)

Lesson topics
Probability and determinism in classical mechanical systems. Bertrand's paradox and its relevance in  physics. The logic of probability (Cox's paper). (link to slides)
Quantum probabilities and Bell's inequalities. Bayes theorem. Example of inference with Bayes theorem. Examples and applications of Bayes' theorem (medical tests, etc.) (link to slides). Bayesian inference, discrete hypotheses, parameter inference.
Bayes factors.  Examples of Bayesian inference: 1. parameter of a binomial model (and Beta pdf posterior).  (link to slides). Link with Max. Likelihood formalism. Examples of Bayesian inference: 2. parameter of a Poisson model (and Gamma pdf posterior); 3. mean value of a Gaussian model (and Gaussian pdf posterior). More on the connection between Bayes' theorem, MLE formalism and least squares. Prior distributions. Jeffreys' method for objective priors. (link to slides) 
Maximum Entropy Method (MEM). The kangaroo problem. "Objective" priors from MEM.  (link to slides). A few examples of Bayesian techniques: 1. straight-line fit. (link to slides)
More examples: 2. weighted mean; 3. systematic errors; 4. search for weak signals in spectra; 5. expert elicitation Example of Bayesian techniques: 6. the lost flight AF 477. (link to slides)
Further applications of Bayesian reasoning: 1. the EM algorithm .2. image processing algorithms.
(link to slides). 
Numerical evaluation methods and Bayesian statistics. Acceptance-rejection sampling; importance sampling; statistical bootstrap; Bayesian methods in a sampling-resampling perspective; introduction to Markov chains. The Metropolis algorithm. The Markov Chain Monte Carlo (MCMC) method. (link to slides)
Bayesian learning. Naive Bayesian classifiers. The AUTOCLASS unsupervised Bayesian classifier.  (link to slides).
date TBD
Exams (talks given by students).

Useful links