  We present a new procedure to determine Parton Distribution Functions (PDFs),
based on Markov Chain Monte Carlo (MCMC) methods. The aim of this paper is to
show that we can replace the standard $\chi^2$ minimization by procedures
grounded on Statistical Methods, and on Bayesian inference in particular, thus
offering additional insight into the rich field of PDFs determination. After a
basic introduction to these technics, we introduce the algorithm we have chosen
to implement -- namely Hybrid (or Hamiltonian) Monte Carlo. This algorithm,
initially developed for Lattice QCD, turns out to be very interesting when
applied to PDFs determination by global analyses; we show that it allows to
circumvent the difficulties due to the high dimensionality of the problem, in
particular concerning the acceptance. A first feasibility study is performed
and presented, which indicates that Markov Chain Monte Carlo can successfully
be applied to the extraction of PDFs and of their uncertainties.
