  We implement a Monte Carlo sampling strategy to extract helicity parton
densities and their uncertainties from a reference set of longitudinally
polarized scattering data, chosen to be that used in the DSSV14 global
analysis. Instead of adopting the simplest possible functional forms for the
helicity parton distributions and imposing certain restrictions on their
parameter space in order to constrain them, we employ redundant, flexible
parametrizations and fit them to a large number of Monte Carlo replicas of the
existing data. The optimum fit and its uncertainty estimates are then assumed
to be given by the statistical average of the obtained ensemble of replicas of
helicity parton densities and their corresponding variance, respectively. We
compare our results to those obtained by the traditional fitting approach and
to the uncertainty estimates derived with the robust Lagrange multiplier
method, finding good agreement. As a first application of our new set of
replicas, we discuss the impact of the recent STAR dijet data in further
constraining the elusive gluon helicity density through the reweighting method.
