Sigma One

TL;DR

This paper shows that it is possible to estimate both the mean and dispersion of a population from a single observation under certain constraints, challenging conventional statistical assumptions.

Contribution

It introduces a method to infer population dispersion from a single data point using physically reasonable bounds, highlighting its relevance in astronomical data modeling.

Findings

Dispersion can be estimated from a single observation.

Physically reasonable constraints enable this estimation.

The approach is applicable to astronomical data modeling.

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.