Bayesian inference of T Tauri star properties using multi-wavelength
  survey photometry
  There are many pertinent open issues in the area of star and planet
formation. Large statistical samples of young stars across star-forming regions
are needed to trigger a breakthrough in our understanding, but most optical
studies are based on a wide variety of spectrographs and analysis methods,
which introduces large biases. Here we show how graphical Bayesian networks can
be employed to construct a hierarchical probabilistic model which allows
pre-main sequence ages, masses, accretion rates, and extinctions to be
estimated using two widely available photometric survey databases (IPHAS
r/i/Halpha and 2MASS J-band magnitudes.) Because our approach does not rely on
spectroscopy, it can easily be applied to homogeneously study the large number
of clusters for which Gaia will yield membership lists. We explain how the
analysis is carried out using the Markov Chain Monte Carlo (MCMC) method and
provide Python source code. We then demonstrate its use on 587 known low-mass
members of the star-forming region NGC 2264 (Cone Nebula), arriving at a median
age of 3.0 Myr, an accretion fraction of 20+/-2% and a median accretion rate of
10^-8.4 Msol/yr. The Bayesian analysis formulated in this work delivers results
which are in agreement with spectroscopic studies already in the literature,
but achieves this with great efficiency by depending only on photometry. It is
a significant step forward from previous photometric studies, because the
probabilistic approach ensures that nuisance parameters, such as extinction and
distance, are fully included in the analysis with a clear picture on any
degeneracies.
