  We discuss the Hessian PDF reweighting - a technique intended to estimate the
effects that new measurements have on a set of PDFs. The method stems
straightforwardly from considering new data in a usual $\chi^2$-fit and it
naturally incorporates also non-zero values for the tolerance,
$\Delta\chi^2>1$. In comparison to the contemporary Bayesian reweighting
techniques, there is no need to generate large ensembles of PDF Monte-Carlo
replicas, and the observables need to be evaluated only with the central and
the error sets of the original PDFs. In spite of the apparently rather
different methodologies, we find that the Hessian and the Bayesian techniques
are actually equivalent if the $\Delta\chi^2$ criterion is properly included to
the Bayesian likelihood function that is a simple exponential.
