Mini course on Statistics in Astronomy

The course runs from February 6th to March 8th, with lectures Tuesday 2 PM and Thursday noon (except during reading week). The course will be taught by Barth Netterfield and Marten van Kerkwijk, with the schedule given below (all lectures in MP 1318A). Some literature is indicated. A more general reference would be Bayesian Logical Data Analysis for the Physical Sciences, by Phil Gregory (2005, Cambridge Univ. Press). It also describes non-Bayesian analysis and shows how for quite general cases the results are very similar.

Tu, Feb 06: Marten
Literature: Numerical Recipes, parts of Chapter 15; BLDAPS, Chapter
- General error propagation.
- Introduction to chi2 fitting, probabilities, number of parameters, degrees of freedom. Estimating expected uncertainties.
- Applications: straight line, etc.
Th, Feb 08: Marten
Literature: Horne, 1986, PASP, 98, 609.
- Determining the optimal way to extract data; thinking clearly about what is actually measured.
- Application to images and spectra.
Tu, Feb 13: Marten
Literature: Numerical Recipes, remainder of Chapter 15; Alard & Lupton, 1998, ApJ, 503, 325; Rucinski, 2002, AJ, 124, 1746.
- General least-squares modelling with base functions.
- Least-squares fitting algorithms
- Applications: optimal image subtraction, rotational line profiles
Th, Feb 15: Barth
- Introduction to Bayesian analysis; (1 parameter), priors.
- Relation with "frequentist" approach.
Tu, Feb 27: Barth
- Non Gaussian likelihoods and error estimates.
- Significance estimates.
Th, Mar 01: Marten
Literature: Cash, 1979, ApJ, 228, 939; for a Bayesian perspective, Gregory & Loredo, 1992, ApJ, 398, 146.
- Poisson errors, maximum likelihood for Poisson-distributed data.
- Pitfalls: Resolution and binning (e.g., for X-ray spectra).
- Pitfalls: number of trials (e.g., source/period finding).
Tu, Mar 06: Barth
- Multi Parameter Baysian, fischer matrix.
- Correlated parameters, marginalization.
Th, Mar 08: Barth
- Monte Carlo analysis, error estimates.
- Relation to Baysian analysis.
- More pitfalls???

For students taking this course for credit: the testing will be by two assignments:

Problem set I, due 1 March 2007 (C programme mentioned in text).
See also the solution, the PSF fitting programme I used, and output from both the Poisson and PSF programmes.
Problem set II, due 4 April 2007. (data set mentioned in text).

Finally, there is a pdf of scans of Marten's notes.

Marten van Kerkwijk / mhvk@astro