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 straight-line 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. Cramér-Rao-Fisher Bound. Boltzmann entropy and Shannon entropy. Kullback-Leibler 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 ill-posed 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
acceptance-rejection 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 sampling-resampling 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.
Affine-invariant 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)