Statistical Methods in Astrophysics
Scanned lecture notes
- Lecture 1 (15.10.2007) (180 kB)
- Lecture 2 (22.10.2007) (190 kB)
- Lecture 3 (29.10.2007) (320 kB)
- Lecture 4 (05.11.2007) (310 kB)
- Lecture 5 (19.11.2007) (180 kB)
- Lecture 6 (26.11.2007) (290 kB)
- Lecture 7 (03.12.2007) (180 kB)
- Lecture 8 (16.12.2007) (330 kB)
- Lecture 9 (07.01.2008) (330 kB)
- Lecture 10 (14.01.2008) (370 kB)
- Lecture 11 (28.01.2008) (176 kB)
- Lecture 12 (04.02.2008) (280 kB) See also the article by S.L. Bridle et. al.
The lecture covers:
1. Basics of Bayesian statistics
2. Parameter Estimation: coin example, gaussian noise and averages, change of variables (the light house example), central limit theorem, amplitude of a signal in presence of background, marginal distributions, binning of data, reliabilities, best estimates, error bars and correlations, maximum likelihood and least squares approximations
3. Cosmic Microwave Background (CMB) mapmaking: from time ordered data to CMB-sky maps, lossless mapmaking
4. The CMB likelihood function
5. Galaxy surveys
6. Computing the signal covariance matrix for a given theoretical model: window functions
7. Estimating the likelihood functions for CMB and galaxy surveys: Karhunen-Loeve method, optimal quadratic estimators
8. The Fisher matrix: limits and applications, forecasting
9. Markov chain monte carlo: principles and the Metropolis algorithm, parameter estimation, cmbeasy
10. Model selection, evidence, hypothesis testing
11. Assigning probabilities: entropy and its application in astronomy
Literature:
- D. S. Sivia, “Data Analysis. A Bayesian Tutorial”
- S. Dodelson, “Modern Cosmology”
- and various research papers …