2015/07/08 by C. A. L. Bailer-Jones · 1 voice
Physics and Astronomy · #astro-ph.GA #astro-ph.IM #astro-ph.SR
paper · pdf · doi:10.1086/683116
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)
arxiv published 2015/07/08 · arxiv created 2015/09/24 · arxiv updated 2016/03/09
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.