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 
8/05/2023 
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)  
9/05/2023  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) 

11/05/2023  Discussion on prior
distributions and random variable transformations. Physical models and prior distributions (Bertrand's paradox). Bartlett identities. CramÃ©rRaoFisher Bound. Boltzmann entropy and Shannon entropy. KullbackLeibler divergence and its properties. Jeffreys' priors. (link to slides) 

12/05/2023  Edwin
Jaynes and the Maximum Entropy (MaxEnt) principle. The
kangaroo problem as an example of illposed problem and
its regularization by entropy maximization. Objective
priors with the maximum entropy method in both the
discrete and the continuous case. Simple example of
application to image restoration (Skilling). Example: uncalibrated Gaussian measurement errors. (link to slides) 

15/05/2023  Examples of application
of the Bayesian approach with less well defined priors:
1. Expert elicitation; 2. the statistical link between
smoking and lung cancer. Applications of Bayesian
methods to Image processing. Monte Carlo methods in the
Bayesian approach, part 1: 1. Review of
acceptancerejection sampling; 2. importance sampling;
3. statistical bootstrap (link
to slides) 

16/05/2023  Monte Carlo methods in the Bayesian approach, part 2: 4. Bayesian methods in a samplingresampling perspective. 5. introduction to Markov chains. (link to slides)  
17/05/2023  Monte Carlo methods in
the Bayesian approach, part 3: 6. Simulated annealing.
7. The Metropolis algorithm. 8. 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. (link to slides) 

18/05/2023  Monte Carlo methods in
the Bayesian approach, part 4: 9. The Gibbs sampler. 10.
Computational efficiency of MCMC methods. 11.
Affineinvariant MCMC. Applications of Bayesian
methods: 1. Bayesian model selection. 2. Bayes and
automatic classification. (link
to slides) 
Useful links
 BLIP (Bayesians Laboring In Physics)
 BUGS Project (Bayesian Inference Using Gibbs Sampling) + WinBUGS + OpenBUGS
 EMCEE
affine invariant MCMC documentation
 International Society for Bayesian Analysis
 JAGS (Just Another
Gibbs Sampler)
 MacMCMC
 Webpage of Larry Bretthorst
 Webpage of Tom Loredo
 Stan
 Statistics
bibliography at SLAC
 Valencia meetings
 Wikipedia (article on Rev. T. Bayes)