Estimating distances from parallaxes

TL;DR

Estimating stellar distances from parallaxes is complex, especially with high fractional errors, and requires careful prior assumptions; the paper evaluates different priors and recommends a simple, effective prior model.

Contribution

The paper analyzes the impact of various priors on distance estimation from parallaxes and proposes a simple prior that improves accuracy and handles non-positive parallaxes.

Findings

Uniform priors lead to large bias and variance.

Sharp cut-off priors have similar issues.

A decreasing prior at infinity performs well and accommodates non-positive parallaxes.

Abstract

Astrometric surveys such as Gaia and LSST will measure parallaxes for hundreds of millions of stars. Yet they will not measure a single distance. Rather, a distance must be estimated from a parallax. In this didactic article, I show that doing this is not trivial once the fractional parallax error is larger than about 20%, which will be the case for about 80% of stars in the Gaia catalogue. Estimating distances is an inference problem in which the use of prior assumptions is unavoidable. I investigate the properties and performance of various priors and examine their implications. A supposed uninformative uniform prior in distance is shown to give very poor distance estimates (large bias and variance). Any prior with a sharp cut-off at some distance has similar problems. The choice of prior depends on the information one has available - and is willing to use - concerning, for example, the survey and the Galaxy. I demonstrate that a simple prior which decreases asymptotically to zero at infinite distance has good performance, accommodates non-positive parallaxes, and does not require a bias correction.