  We describe preliminary results from an effort to quantify the uncertainties
in parton distribution functions and the resulting uncertainties in predicted
physical quantities. The production cross section of the $W$ boson is given as
a first example. Constraints due to the full data sets of the CTEQ global
analysis are used in this study. Two complementary approaches, based on the
Hessian and the Lagrange multiplier method respectively, are outlined. We
discuss issues on obtaining meaningful uncertainty estimates that include the
effect of correlated experimental systematic uncertainties and illustrate them
with detailed calculations using one set of precision DIS data.
