Jul 9th, 2008| 01:00 pm | Posted by vlk

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)’ »

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13 Comments
Jul 16th, 2007| 03:31 pm | Posted by hlee

From arxiv/astro-ph:0707.2064v1

**Star Formation via the Little Guy: A Bayesian Study of Ultracool Dwarf Imaging Surveys for Companions ** by P. R. Allen.

I rather skip all technical details on ultracool dwarfs and binary stars, reviews on star formation studies, like initial mass function (IMF), astronomical survey studies, which Allen gave a fair explanation in arxiv/astro-ph:0707.2064v1 but want to emphasize that based on simple **Bayes’ rule** and careful set-ups for **likelihoods** and **priors** according to data (ultracool dwarfs), quite informative conclusions were drawn:

Continue reading ‘[ArXiv] Bayesian Star Formation Study, July 13, 2007’ »

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1 Comment
Jun 27th, 2007| 02:23 pm | Posted by hlee

From arXiv:physics.data-an/0706.3622v1:

**Comments on the unified approach to the construction of classical confidence intervals**

This paper comments on classical confidence intervals and upper limits, as the so-called a flip-flopping problem, both of which are related asymptotically (when n is large enough) by the definition but cannot be converted from one to the another by preserving the same coverage due to the poisson nature of the data.

Continue reading ‘[ArXiv] Classical confidence intervals, June 25, 2007’ »