  The Bayesian reweighting procedure is applied for the first time to a TMD
distribution, the quark Sivers function extracted from SIDIS data. By
exploiting the recent published single spin asymmetry data for the inclusive
jet production in $p^\uparrow p$ collisions from the STAR collaboration at
RHIC, we show how such a procedure allows to incorporate the information
contained in the new data set, without the need of re-fitting, and to explore a
much wider $x$ region compared to SIDIS measurements. The reweighting method is
also extended to the case of asymmetric errors, and the results show a
significant improvement on the knowledge of the quark Sivers function.
