Bayesian approach to estimating stellar properties and interstellar extinction law based on photometry

We describe Bayesian probabilistic approach to estimating the properties of stars and the interstellar extinction law based on photometric observations and using prior data about the parameters of the stars. The accuracy of the resulting estimates is analyzed in the case of SDSS and 2MASS surveys. We found that our estimates have no systematic deviations in the case of photometric accuracy typical of the surveys considered and errors of prior data of ΔT _eff = ±150 K and Δ_{log g} = ±0.5. Note that the error of the estimated interstellar extinction A ₀ is of about 0_. ^m 3, and the error of the R ₀ estimate depends on extinction and is close 0.2 for moderate A0 values. The fractional error of the estimated stellar angular diameters is close to 10%. A possible application of our approach is to determine the dependence of interstellar extinction on distance using stars closely located in the same sky area.