Sigma One
arXiv:1004.0448 · doi:10.1088/0004-6256/139/5/2052
Abstract
We demonstrate that it is possible to calculate not only the mean of an underlying population but also its dispersion, given only a single observation and physically reasonable constraints (i.e., that the quantities under consideration are non-negative and bounded). We suggest that this counter-intuitive conclusion is in fact at the heart of most modeling of astronomical data.
Accepted to the Astronomical Journal. 13 pages, 4 figures