  We present a determination of a set of polarized parton distributions (PDFs)
of the nucleon, at next-to-leading order, from a global set of longitudinally
polarized deep-inelastic scattering data: NNPDFpol1.0. The determination is
based on the NNPDF methodology: a Monte Carlo approach, with neural networks
used as unbiased interpolants, previously applied to the determination of
unpolarized parton distributions, and designed to provide a faithful and
statistically sound representation of PDF uncertainties. We present our
dataset, its statistical features, and its Monte Carlo representation. We
summarize the technique used to solve the polarized evolution equations and its
benchmarking, and the method used to compute physical observables. We review
the NNPDF methodology for parametrization and fitting of neural networks, the
algorithm used to determine the optimal fit, and its adaptation to the
polarized case. We finally present our set of polarized parton distributions.
We discuss its statistical properties, test for its stability upon various
modifications of the fitting procedure, and compare it to other recent
polarized parton sets, and in particular obtain predictions for polarized first
moments of PDFs based on it. We find that the uncertainties on the gluon, and
to a lesser extent the strange PDF, were substantially underestimated in
previous determinations.
