The eROSITA Final Equatorial-Depth Survey (eFEDS). The stellar
  counterparts of eROSITA sources identified by machine learning and Bayesian
  algorithms
  Stars are ubiquitous X-ray emitters and will be a substantial fraction of the
X-ray sources detected in the on-going all-sky survey performed by the eROSITA
instrument aboard the Spectrum Roentgen Gamma (SRG) observatory. We use the
X-ray sources in the eROSITA Final Equatorial-Depth Survey (eFEDS) field
observed during the SRG performance verification phase to investigate different
strategies to identify the stars among other source categories. We focus here
on Support Vector Machine (SVM) and Bayesian approaches, and our approaches are
based on a cross-match with the Gaia catalog, which will eventually contain
counterparts to virtually all stellar eROSITA sources. We estimate that 2060
stars are among the eFEDS sources based on the geometric match distance
distribution, and we identify the 2060 most likely stellar sources with the SVM
and Bayesian methods, the latter being named HamStars in the eROSITA context.
Both methods reach completeness and reliability percentages of almost 90%, and
the agreement between both methods is, incidentally, also about 90%. Knowing
the true number of stellar sources allowed us to derive association
probabilities $p_{ij}$ for the SVM method similar to the Bayesian method so
that one can construct samples with defined completeness and reliability
properties using appropriate cuts in $p_{ij}$. The thus identified stellar
sources show the typical characteristics known for magnetically active stars,
specifically, they are generally compatible with the saturation level, show a
large spread in activity for stars of spectral F to G, and have comparatively
high fractional X-ray luminosities for later spectral types.
