  The reweighting procedure that using Bayesian statistics incorporates the
information contained in a new data set, without the need of re-fitting, is
applied to the quark Sivers function extracted from Semi-Inclusive Deep
Inelastic Scattering (SIDIS) data. We exploit the recently published single
spin asymmetry data for the inclusive jet production in polarized $pp$
collisions from the STAR Collaboration at RHIC, which cover a much wider $x$
region compared to SIDIS measurements. The reweighting method is extended to
the case of asymmetric errors and the results show a remarkable improvement of
the knowledge of the quark Sivers function.
