  The current scientific standard in PDF uncertainty estimation relies either
on repeated fits over artificially generated data to arrive at Monte Carlo
samples of best fits or on the Hessian method, which uses a quadratic expansion
of the figure of merit, the $\chi^2$-function. Markov Chain Monte Carlo methods
allows one to access the uncertainties of PDFs without making use of quadratic
approximations in a statistically sound procedure while at the same time
preserving the correspondence between the sample and $\chi^2$-value. Rooted in
Bayesian statistics the $\chi^2$-function is repeatedly sampled to obtain a set
of PDFs that serves as a representation of the statistical distribution of the
PDFs in their function space. After removing the dependence between the samples
(the so-called autocorrelation) the set can be used to propagate the
uncertainties to physical observables. The final result is an independent
procedure to obtain PDF uncertainties that can be confronted by the
state-of-the-art in order to ultimately arrive at a better understanding of the
proton's structure.
