The AstroStat Slog

The Kaplan-Meier (K-M) estimator is the non-parametric maximum likelihood estimator of the survival probability of items in a sample. “Survival” here is a historical holdover because this method was first developed to estimate patient survival chances in medicine, but in general it can be thought of as a form of cumulative probability. It is of great importance in astronomy because so much of our data are limited and this estimator provides an excellent way to estimate the fraction of objects that may be below (or above) certain flux levels. The application of K-M to astronomy was explored in depth in the mid-80′s by Jurgen Schmitt (1985, ApJ, 293, 178), Feigelson & Nelson (1985, ApJ 293, 192), and Isobe, Feigelson, & Nelson (1986, ApJ 306, 490). [See also Hyunsook's primer.] It has been coded up and is available for use as part of the ASURV package. Continue reading ‘Kaplan-Meier Estimator (Equation of the Week)’ »

Astronomers confront with various censored and truncated data. Often these types of data are called after famous scientists who generalized them, like Eddington bias. When these censored or truncated data become the subject of study in statistics, instead of naming them, statisticians try to model them so that the uncertainty can be quantified. This area is called survival analysis. If your library has The American Statistician subscription and you are an astronomer handles censored or truncated data sets, this primer would be useful for briefly conceptualizing statistics jargon in survival analysis and for characterizing uncertainties residing in your data. Continue reading ‘Survival Analysis: A Primer’ »