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The Bayesian reweighting procedure is applied for the first time to a TMDdistribution, the quark Sivers function extracted from SIDIS data. Byexploiting the recent published single spin asymmetry data for the inclusivejet production in $p^\uparrow p$ collisions from the STAR collaboration atRHIC, we show how such a procedure allows to incorporate the informationcontained in the new data set, without the need of re-fitting, and to explore amuch wider $x$ region compared to SIDIS measurements. The reweighting method isalso extended to the case of asymmetric errors, and the results show asignificant improvement on the knowledge of the quark Sivers function.

Reweighting the quark Sivers function with STAR jet data