# 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 |

17/04/2020 |
Bayes theorem. Example of
inference with Bayes theorem. Examples and applications of
Bayes' theorem (medical tests, etc.). Bayesian inference,
discrete hypotheses, parameter inference. Example of Bayesian inference: parameter of a binomial model (and Beta pdf posterior). Cromwell's rule (Lindley). Bayesian credible intervals. (link to slides) |

20/04/2020 | A decision problem (from
Skilling, 1998). Analytical Bayesian straight-line fit.
Discussion on prior distributions and random variable
transformations. Physical models and prior distributions
(physical coin toss, Bertrand's paradox). Jeffreys' priors. (link
to slides) |

23/04/2020 | Boltzmann entropy and Shannon
entropy. Edwin Jaynes and his approach to statistical mechanics.
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 (using the KL divergence). Simple example of
application to image restoration (Skilling). (link
to slides) |

24/04/2020 | Examples of
application of the Bayesian approach: 1. weighted mean; 2.
miscalibrated Gaussian measurement errors; 3. search for weak
signals in spectra; 4. expert elicitation; 5. the lost flight AF
477 and other search problems; 6. the statistical link between
smoking and lung cancer. (link to
slides) |

30/04/2020 | Monte Carlo methods in the
Bayesian approach, part 1. 1. Review of the acceptance-rejection
sampling; 2. importance sampling; 3. statistical bootstrap; 4.
Bayesian methods in a sampling-resampling perspective; 5.
introduction to Markov chains. (link
to slides) |

01/05/2020 | Monte Carlo methods in the Bayesian approach, part 2. The Markov Chain Monte Carlo (MCMC). (link to slides). A few examples of the MCMC at work. (link to slides) |

04/05/2020 | Applications of Bayesian methods.
1. Image restoration; 2. Bayes and automatic classification. 3.
Bayesians, frequentists and all that, a discussion on the
principles of statistics. (link to
slides) |

05/05/2020 | Applications of Bayesian methods.
4. The EM algorithm; 5. The mass distribution of neutron stars.
(link to slides) |

# 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
- MacMCMC
- Webpage of Larry Bretthorst
- Webpage of Tom Loredo
- Statistics
bibliography as SLAC

- Valencia meetings
- Wikipedia (article on Rev. T. Bayes)