We introduce the Hessian reweighting of parton distribution functions (PDFs).
Similarly to the better-known Bayesian methods, its purpose is to address the
compatibility of new data and the quantitative modifications they induce within
an existing set of PDFs. By construction, the method discussed here applies to
the PDF fits that carried out a Hessian error analysis using a non-zero
tolerance $\Delta\chi^2$. The principle is validated by considering a simple,
transparent example. We are also able to establish an agreement with the
Bayesian technique provided that the tolerance criterion is appropriately
accounted for and that a purely exponential Bayesian likelihood is assumed. As
a practical example, we discuss the inclusive jet production at the LHC.Comment: The final version, to appear in JHE