Distance and extinction determination for APOGEE stars with Bayesian
  method
  Using a Bayesian technology we derived distances and extinctions for over
100,000 red giant stars observed by the Apache Point Observatory Galactic
Evolution Experiment (APOGEE) survey by taking into account spectroscopic
constraints from the APOGEE stellar parameters and photometric constraints from
2MASS, as well as a prior knowledge on the Milky Way. Derived distances are
compared with those from four other independent methods, the Hipparcos
parallaxes, star clusters, APOGEE red clump stars, and asteroseismic distances
from APOKASC (Rodrigues et al. 2014) and SAGA Catalogues (Casagrande et al.
2014). These comparisons covers four orders of magnitude in the distance scale
from 0.02 kpc to 20 kpc. The results show that our distances agree very well
with those from other methods: the mean relative difference between our
Bayesian distances and those derived from other methods ranges from -4.2% to
+3.6%, and the dispersion ranges from 15% to 25%. The extinctions toward all
stars are also derived and compared with those from several other independent
methods: the Rayleigh-Jeans Color Excess (RJCE) method, Gonzalez's
two-dimensional extinction map, as well as three-dimensional extinction maps
and models. The comparisons reveal that, overall, estimated extinctions agree
very well, but RJCE tends to overestimate extinctions for cool stars and
objects with low logg.
