Bayesian isochrone fitting and stellar ages
  Stellar evolution theory has been extraordinarily successful at explaining
the different phases under which stars form, evolve and die. While the
strongest constraints have traditionally come from binary stars, the advent of
asteroseismology is bringing unique measures in well-characterised stars. For
stellar populations in general, however, only photometric measures are usually
available, and the comparison with the predictions of stellar evolution theory
have mostly been qualitative. For instance, the geometrical shapes of
isochrones have been used to infer ages of coeval populations, but without any
proper statistical basis. In this chapter we provide a pedagogical review on a
Bayesian formalism to make quantitative inferences on the properties of single,
binary and small ensembles of stars, including unresolved populations. As an
example, we show how stellar evolution theory can be used in a rigorous way as
a prior information to measure the ages of stars between the ZAMS and the
Helium flash, and their uncertainties, using photometric data only.
