Phd in Physics

Bayesan inference

Bayesan inference

Academic year 2021/2022

Sommario del corso

• Course objectives
• Program
• Suggested textbooks and readings
• Notes
• Teaching tools

Course objectives

This short course will touch upon a number of topics in the framework of Bayesian inference for data analysis.  The first and foremost aim will be to understand the general problem of estimating parameters from data.  This will be done in the context of forecast, introducing the information matrix to analyse experimental designs before any data are taken, to assess how the experiment will actually perform.  Then, numerical methods for estimating parameters from data will be introduced in the form of Markov chain Monte Carlo methods.  Finally, the problem of model selection will be briefly discussed.

Program

• Fundaments of Bayesian inference
• Hypothesis testing, parameter estimation, model selection
• Posterior probability, likelihood, prior, and evidence
• Marginal vs conditional errors
• The characteristic function
• The information matrix
• The Cramer-Rao bound
• Properties of the information matrix
• Application to a real-world example (Cavendish experiment)
• Markov chain Monte Carlo methods
• Model selection

• A.F. Heavens, Statistical techniques in cosmology, https://arxiv.org/abs/0906.0664
• L. Verde, A practical guide to Basic Statistical Techniques for Data Analysis in Cosmology, https://arxiv.org/abs/0712.3028
• C. Ferrie & S. Kaiser, Bayesian Probability for Babies, Sourcebooks Inc. (2019)

Note

Timetable

* Fri 3rd June, 11-13;
* Mon 6th June, 14-16;
* Tue 7th June, 14-16;
* Thu 9th June, 9-11.

• Teaching materials
• Exams and finals
• Go to Moodle
• Visit the forums