Ruprecht Karls Universität Heidelberg

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Statistical Methods in Astrophysics

Scanned lecture notes

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 …

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