Marginal likelihoods of distances and extinctions to stars: computation
  and compact representation
  We present a method for obtaining the likelihood function of distance and
extinction to a star given its photometry. The other properties of the star
(its mass, age, metallicity and so on) are marginalised assuming a simple
Galaxy model. We demonstrate that the resulting marginalised likelihood
function can be described faithfully and compactly using a Gaussian mixture
model. For dust mapping applications we strongly advocate using monochromatic
over bandpass extinctions, and provide tables for converting from the former to
the latter for different stellar types.
