Some Useful Statistics Papers for Astronomers (a work in progress)
These are some astrostatistics papers which should be in your personal library. These are just a handful of my favorites. If you have any other suggestions, please pass them along to me.
Particularly Broad Statistics Discussions
Penn State Center for Astrostatistics
Kelly (2007) "Some Aspects of Measurement Error in Linear Regression of Astronomical Data" Astrophys. Jrnl. 665, 1489: Describes "a Bayesian method to account for measurement errors in linear regression of astronomical data".
Mean, Median, Standard Deviation, etc.
Gott et al. (2001) "Median Statistics, H_o, and the Accelerating Universe" Astrophys. Jrnl. 549, 1: All hail the median and the uncertainty of the median! Excellent paper for astronomers, whose data are often plagued with "million-pound penguins".
Muller (2000) "Possible Advantages of a Robust Evaluation of Comparisons", Journal of Research of the National Institute of Standards and Technology, 105, 551: median statistics, "median of the absolute deviation" (MAD),
Lutz & Upgren (1980) "An analysis of parallaxes determined in two coordinates" Astronomical Journal 85, 1390: An introduction to estimating standard deviations via probability plots (i.e. a way of estimating "sigma" that is largely immune to the deleterious effects of outliers).
Chi-squared Fitting
Lampton, Margon, & Bowyer (1976) "Parameter Estimation in X-ray Astronomy" Astrophys. Jrnl. 208, 177 and Avni (1976) "Energy spectra of X-ray clusters of galaxies" Astrophys. Jrnl. 210, 642: Both studies discuss at length the estimation of the uncertainties in fitted parameters in chi^2 fitting.
Gould (2003) "chi^2 and Linear Fits" arXiv:astro-ph/0310577: "The mathematics of linear fits is presented in covariant form. Topics include: correlated data, covariance matrices, joint fits to multiple data sets, constraints, and extension of the formalism to non-linear fits. A brief summary at the end provides a convenient crib sheet. These are somewhat amplified notes from a 90 minute lecture in a first-year graduate course. None of the results are new. They are presented here because they do not appear to be elsewhere available in compact form.
Linear Regressions (Line Fitting)
Isobe et al. (1990) "Linear regression in astronomy" Astrophys. Jrnl. 364, 104: Shows several different ways of fitting lines, and some of the pitfalls.
Wall (1996) "Practical Statistics for Astronomers: II. Correlation, Data-Modelling and Sample Comparison".
Censored Data (Dealing with Upper & Lower Limits)
Feigelson & Nelson (1985) "Statistical methods for astronomical data with upper limits. I - Univariate distributions" Astrophysical Jrnl 293, 192
Isobe, Feigelson, & Nelson (1986) "Statistical methods for astronomical data with upper limits. II - Correlation and regression" Astrophysical Journal 306, 490
Small Number Statistics
Gehrels (1986) "Confidence limits for small numbers of events in astrophysical data" Astrophysical Journal 303, 386: Assigning uncertainties when you are in the regime of having a small number of counts (every X-ray astronomer must read this!).
Monte Carlo
Marsaglia
(1972) "Choosing a Point from the Surface of a Sphere"
Ann. Math. Stat. 43, 645: A frequent problem in Monte Carlo is that
of sampling uniformly from the surface of the unit 3-sphere... I found this useful for simulating
orbits of companions of stars at random angles.