  An important limitation in current fits of parton distribution functions
(PDFs) is that PDF uncertainties do not include any source of theoretical
uncertainty. Here we present a general method for incorporating theoretical
uncertainties into PDF fits, focussing in particular on perturbative missing
higher order uncertainties (MHOUs). We consider two methods for estimating the
effect of MHOUs on PDFs, both based on scale variations. Firstly, we present
PDF fits based on theoretical predictions with varied scales, and use these to
estimate the associated MHOUs. Secondly, we discuss the construction of a
theoretical covariance matrix using scale variations, and its combination with
the experimental covariance matrix currently used in PDF fits.
