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.