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Oggetto:

Bayesan inference

Oggetto:

Bayesan inference

Oggetto:

Academic year 2021/2022

Teacher
Prof. Stefano Camera
Degree course
PhD in Physics
Year
1st year, 2nd year, 3rd year
Teaching period
Second semester
Type
Other activities
Credits/Recognition
2
Course disciplinary sector (SSD)
FIS/05 - astronomy and astrophysics
Delivery
Formal authority
Language
English
Attendance
Obligatory
Type of examination
Oral
Oggetto:

Sommario del corso

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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 forecasts, 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.

Oggetto:

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

Suggested readings and bibliography

Oggetto:

  • 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)


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Notes

Timetable

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

Enroll
  • Closed
    Enrollment opening date
    31/01/2022 at 12:00
    Enrollment closing date
    31/05/2022 at 12:00
    Oggetto:
    Last update: 04/11/2022 18:11
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