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)Date 
Lesson topics 
24/9/2018 
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)

24/9/2018 
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. 
25/9/2018 
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) 
25/9/2018 
Maximum Entropy Method (MEM). The kangaroo problem. "Objective" priors from MEM. (link to slides). A few examples of Bayesian techniques: 1. straightline fit. (link to slides) 
27/9/2018 
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) 
27/9/2018 
Further applications of Bayesian
reasoning: 1. the EM algorithm .2. image processing algorithms. (link to slides). 
28/9/2018 
Numerical evaluation methods and
Bayesian statistics. Acceptancerejection sampling; importance
sampling; statistical bootstrap; Bayesian methods in a
samplingresampling 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
 AUTOCLASS
 Bayesian Inference for the Physical Sciences
 BLIP (Bayesians Laboring In Physics)
 BUGS Project
(Bayesian Inference Using Gibbs Sampling)
 International Society for Bayesian Analysis
 Los Alamos Center for
Bayesian Methods in Environment, Safety, and Health
 Webpage of Larry Bretthorst
 Webpage of Tom Loredo
 Statistics
bibliography as SLAC
 Valencia meetings
 Wikipedia (article on Rev. T. Bayes)