Bayesian inference of stellar parameters and interstellar extinction
  using parallaxes and multiband photometry
  Astrometric surveys provide the opportunity to measure the absolute
magnitudes of large numbers of stars, but only if the individual line-of-sight
extinctions are known. Unfortunately, extinction is highly degenerate with
stellar effective temperature when estimated from broad band optical/infrared
photometry. To address this problem, I introduce a Bayesian method for
estimating the intrinsic parameters of a star and its line-of-sight extinction.
It uses both photometry and parallaxes in a self-consistent manner in order to
provide a non-parametric posterior probability distribution over the
parameters. The method makes explicit use of domain knowledge by employing the
Hertzsprung--Russell Diagram (HRD) to constrain solutions and to ensure that
they respect stellar physics. I first demonstrate this method by using it to
estimate effective temperature and extinction from BVJHK data for a set of
artificially reddened Hipparcos stars, for which accurate effective
temperatures have been estimated from high resolution spectroscopy. Using just
the four colours, we see the expected strong degeneracy (positive correlation)
between the temperature and extinction. Introducing the parallax, apparent
magnitude and the HRD reduces this degeneracy and improves both the precision
(reduces the error bars) and the accuracy of the parameter estimates, the
latter by about 35%. The resulting accuracy is about 200K in temperature and
0.2mag in extinction. I then apply the method to estimate these parameters and
absolute magnitudes for some 47000 F,G,K Hipparcos stars which have been
cross-matched with 2MASS. The method can easily be extended to incorporate the
estimation of other parameters, in particular metallicity and surface gravity,
making it particularly suitable for the analysis of the 10^9 stars from Gaia.
