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 
links 
9/05/2022 
Bayes theorem. Example of inference with Bayes theorem. Examples and applications of Bayes' theorem (medical tests, etc.). Bayesian inference, discrete hypotheses, parameter inference. (link to slides)  
10/05/2022  Example of Bayesian
inference: parameter of a binomial model (and Beta pdf
posterior). Cromwell's rule (Lindley). Bayesian credible
intervals. A decision problem (from Skilling, 1998).
Analytical Bayesian straightline fit. (link to slides) 

11/05/2022  Discussion on prior
distributions and random variable transformations.
Physical models and prior distributions (Bertrand's
paradox). Jeffreys' priors. Boltzmann entropy and
Shannon entropy. Edwin Jaynes and the Maximum Entropy
(MaxEnt) principle. The kangaroo problem as an example
of illposed problem and its regularization by entropy
maximization. (link to slides) 

12/05/2022  Objective
priors with the maximum entropy method in both the
discrete and the continuous case (using the KL
divergence). Simple example of application to image
restoration (Skilling). Examples of application of the Bayesian approach: 1. miscalibrated Gaussian measurement errors. 2. the statistical link between smoking and lung cancer. (link to slides) 

16/05/2022  Examples of application
of the Bayesian approach (ctd.): 3. Expert elicitation.
Monte Carlo methods in the Bayesian approach, part 1: 1. Review of the acceptancerejection sampling; 2. importance sampling; 3. statistical bootstrap; 4. Bayesian methods in a samplingresampling perspective; (link to slides) 

17/05/2022  Monte Carlo methods in the Bayesian approach, part 2. 5. introduction to Markov chains. (link to slides)  
18/05/2022  6. The Markov Chain Monte
Carlo (MCMC). Examples of MCMC at work (parameters of
surviving fraction models in the irradiation of human
cells; Bayesian line fit). MCMC software. Applications of Bayesian methods to Image processing (link to slides) 

19/05/2022  Applications of Bayesian
methods to Image processing (ctd). Example of
application of Bayesian image processing methods to the
reconstruction of galactic/intergalactic mass
distributions from gravitational lensing. Applications
of Bayesian methods: 1. Bayes and automatic
classification. 2. Logit regression. 3. Bayesian model
selection. 4. The EM algorithm. (link
to slides) 
Useful links
 AUTOCLASS
 BLIP (Bayesians Laboring In Physics)
 BUGS
Project (Bayesian Inference Using Gibbs Sampling) + WinBUGS
+ OpenBUGS
 International Society for Bayesian Analysis
 JAGS (Just Another
Gibbs Sampler)
 MacMCMC
 Webpage of Larry Bretthorst
 Webpage of Tom Loredo
 Stan
 Statistics
bibliography as SLAC
 Valencia meetings
 Wikipedia (article on Rev. T. Bayes)