  We develop a general method to quantify the uncertainties of parton
distribution functions and their physical predictions, with emphasis on
incorporating all relevant experimental constraints. The method uses the
Hessian formalism to study an effective chi-squared function that quantifies
the fit between theory and experiment. Key ingredients are a recently developed
iterative procedure to calculate the Hessian matrix in the difficult global
analysis environment, and the use of parameters defined as components along
appropriately normalized eigenvectors. The result is a set of 2d Eigenvector
Basis parton distributions (where d=16 is the number of parton parameters) from
which the uncertainty on any physical quantity due to the uncertainty in parton
distributions can be calculated. We illustrate the method by applying it to
calculate uncertainties of gluon and quark distribution functions, W boson
rapidity distributions, and the correlation between W and Z production cross
sections.
