Chapitres
- Principle of probability
- Classical statistics vs Bayesian
- Likelihood, prior and posterior
- Bayes theorem: meaning and application
- Bayesian inference
- MCMC
- Hierarchical models
- Bayesian model selection: theory
- Bayesian model selection vs hypothesis testingensing basics
Résumé
| These
lectures will give a short introduction to the fundamentals of Bayesian
inference and its application to simple but representative problems.
Numerical methods such as Markov Chain Monte Carlo will be introduced
and their practical workings illustrated. The Bayesian approach to
model selection via Bayesian model comparison will be explained and
contrasted with Frequentist hypothesis testing. |
Bibliographie
- Theory and philosophy of Bayesian vs Frequentist framework:
- "Bayes in the sky: Bayesian inference and model selection in cosmology"
R. Trotta (2008) Invited review, Contemporary Physics, 49, No. 2,
March-April 2008, 71-104 http://arxiv.org/abs/0803.4089 Section 2
- G. Cowan, Physics Today, 82, 2007 http://www.pp.rhul.ac.uk/~cowan/stat/GDCPhysicsToday.pdf
- "Why isn't every physicist a Bayesian?"
Robert
D. Cousins, (UCLA) . UCLA-HEP-94-005, Sep 1994. 27pp. Published in
Am.J.Phys.63:398,1995.
http://ajp.aapt.org/resource/1/ajpias/v63/i5/p398_s1
- Philosophy
and practice of Bayesian statistics: Gelman & Shalizi, 2011
(unpublished)
http://www.stat.columbia.edu/~gelman/research/unpublished/philosophy.pdf
- Likelihood etc:
- "Bayesian logical data analysis for the physical sciences"
P. Gregory, CUP (2003)
- Probability and Measurement Uncertainty in Physics - a Bayesian Primer
G. D’Agostini,(1995), hep-ph/9512295 available here: http://arxiv.org/abs/hep-ph/9512295
- Bayesian methods in astronomy:
- Further reading:
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