Uni Heidelberg: Theoretische Physik: L. Amendola

# Prof.  Luca Amendola

Institut für Theoretische Physik -- Universität Heidelberg

Philosophenweg 16 -- D-69120 Heidelberg -- Germany

Tel: +49-6221-549-407 -- Fax: +49-6221-549-333

Sprechstunde: After my lectures
and by appointment Tuesday 11.00 - 12.00 a.m. (other times also possible)

Bayesian Statistical Methods in Physics and Astrophysics

### Winter Semester 2016/17

The course is an introduction to Bayesian statistical methods in Physics and Astrophysics
CREDITS: 2 (oral exam on the program or, alternatively, seminar on some selected topic; exam by appointment; see below for the detailed program)

Program

- Introduction to probability: definitions, joint and disjoint probability, conditional prob.,
moments, transf. of variables, Binomial, Poissonian, Gaussian, multivariate prob., examples
- Estimation of parameters
Max. Lik. estimators
Bayes' theorem
Likelihood method, conf. regions, marginalization
examples
Sampling the likelihood: grid versus montecarlo
- From the likelihood to the Fisher matrix
Fisher manipulation
Figure of Merit
examples
- General Fisher matrix for gaussian variables
- Two-point statistics
correlation function and power spectrum
higher-order statistics
- Fisher matrix for the power spectrum
examples from the Euclid satellite survey
- Fisher matrix for weak lensing
- Principal component analysis
Model selection, evidence
robustness
Beyond the Fisher matrix
General linear fitting
Frequentist methods, parametric and non-parametric

NOTE: Course begins on October 24th, 2016 (more info)

classes on Monday at 14:15-16:00 Philosophenweg 12, R106

Calendar :
24.10
31.10
07.11
14.11
21.11
28.11
05.12
12.12
19.12 ATTENTION: moved to SR at Philosophenweg 19
09.01
16.01
23.01

Program:

Lecture notes Chap. 1-7, except sections 3.8, 3.11, 3.12, 5.8, 5.9, 6.6, 7.3, 7.5, 7.8, 7.9, 7.10.

Suggested texts:

Lecture notes version 01/2017
L. Amendola and S. Tsujikawa, Dark Energy, Theory and Observations, Cambridge University Press, 2010,
chapters 3 and 13
R. Trotta,Bayes in the sky: Bayesian inference and model selection in cosmology,
P. Gregory, Bayesian Logical Data Analysis for the Physical Sciences, Cambridge University Press

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