  Determinations of structure functions and parton distribution functions have
been recently obtained using Monte Carlo methods and neural networks as
universal, unbiased interpolants for the unknown functional dependence. In this
work the same methods are applied to obtain a parametrization of polarized Deep
Inelastic Scattering (DIS) structure functions. The Monte Carlo approach
provides a bias--free determination of the probability measure in the space of
structure functions, while retaining all the information on experimental errors
and correlations. In particular the error on the data is propagated into an
error on the structure functions that has a clear statistical meaning. We
present the application of this method to the parametrization from polarized
DIS data of the photon asymmetries $A_1^p$ and $A_1^d$ from which we determine
the structure functions $g_1^p(x,Q^2)$ and $g_1^d(x,Q^2)$, and discuss the
possibility to extract physical parameters from these parametrizations. This
work can be used as a starting point for the determination of polarized parton
distributions.
