# Mini course on Statistics in Astronomy (2013)

## Syllabus

Lectures
Jan 25–Feb 15: F11, AB 113; after reading week: TBD.
Lecturers
Barth Netterfield and Marten van Kerkwijk
Web page
`http://www.astro.utoronto.ca/~mhvk/STATMINI/`
Course texts
As given below, but a general reference would be Bayesian Logical Data Analysis for the Physical Sciences (BLDAPS), by Phil Gregory (2005, Cambridge Univ. Press). This text also describes non-Bayesian analysis and shows how for quite general cases the results are very similar. See also a pdf scan of Marten's notes.
Evaluation
For students taking this course for credit: the testing will be by two assignments.
1. Problem set 1 (pdf), due 1 March 2013
2. To come

## Schedule

### Fri, Jan 25 (Marten)

Literature: Numerical Recipes, parts of Chapter 15; BLDAPS 5, 6

• General error propagation.
• Introduction to χ2 fitting, probabilities, number of parameters, degrees of freedom. Estimating expected uncertainties.
• Applications: straight line, etc.

### Fri Feb 1 (Barth)

• Introduction to Bayesian analysis; (1 parameter), priors.
• Relation with "frequentist" approach.

### Fri Feb 8 (Marten;

Literature: Horne 1986PASP…98..609H: An optimal extraction algorithm for CCD spectroscopy.

• Determining the optimal way to extract data; thinking clearly about what is actually measured.
• Application to images and spectra.

### Fri Feb 15 (Marten)

Literature: Numerical Recipes, remainder of Chapter 15; Alard & Lupton, 1998ApJ…503..325A: A Method for Optimal Image Subtraction; Rucinski 2002AJ….124.1746R: Radial Velocity Studies of Close Binary Stars. VII. Methods and Uncertainties.

• General least-squares modelling with base functions.
• Least-squares fitting algorithms
• Applications: optimal image subtraction, rotational line profiles

### Fri Mar 1 (Barth)

• Non Gaussian likelihoods and error estimates.
• Significance estimates.

### Fri Mar 8 (Marten)

Literature: Cash 1979ApJ…228..939C: Parameter estimation in astronomy through application of the likelihood ratio; for a Bayesian perspective, Gregory & Loredo 1992ApJ…398..146G: A new method for the detection of a periodic signal of unknown shape and period.

• 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).

### Fri Mar 15 (Barth)

• Multi Parameter Baysian, Fischer matrix.
• Correlated parameters, marginalization.

### Fri Mar 22 (Barth)

• Monte Carlo analysis, error estimates.
• Relation to Baysian analysis.
• More pitfalls??

Date: 2013-02-22 14:32:02 EST

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