Estimating Distances from 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 cutoff 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 nonpositive parallaxes, and does not require a bias correction.
 Publication:

Publications of the Astronomical Society of the Pacific
 Pub Date:
 October 2015
 DOI:
 10.1086/683116
 arXiv:
 arXiv:1507.02105
 Bibcode:
 2015PASP..127..994B
 Keywords:

 Astrophysics  Instrumentation and Methods for Astrophysics;
 Astrophysics  Astrophysics of Galaxies;
 Astrophysics  Solar and Stellar Astrophysics
 EPrint:
 To appear as a tutorial article in the October 2015 issue (vol. 127) of Publications of the Astronomical Society of the Pacific (http://www.jstor.org/stable/10.1086/683116)