MYStIX project: Bayesian matching

This high stellar density makes it inevitable that a large fraction of X-ray positions will have a faint field star close to them, which standard matching techniques may incorrectly take to be the counterpart. Instead we use the infrared data to create a model of both the field star and counterpart magnitude distributions, which we then combine with a Bayesian technique to yield a probability that any star is the counterpart of an X-ray source.

In our more crowded fields, between 10% and 20% of counterparts that would be identified on the grounds of being the closest star to an X-ray position within a 99% confidence error circle are instead identified by the Bayesian technique as field stars. These stars are preferentially concentrated at faint magnitudes. Equally importantly the technique also gives a probability that the true counterpart to the X-ray source falls beneath the magnitude limit of the infrared catalog.