# Estimating distances from parallaxes: a tutorial

### C.A.L. Bailer-Jones

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.

A tutorial article in Publications of the Astronomical Society of the Pacific, 127, 994 (2015)

[PDF] [ADS] [arXiv] [journal link]

Gaia *Image of the week* (24 September 2015)

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Coryn Bailer-Jones, calj at mpia-hd.mpg.de

Last modified: 24 September 2015