  Parton distribution functions (PDFs) form an essential part of particle
physics calculations. Currently, the most precise predictions for these
non-perturbative functions are generated through fits to global data. A problem
that several PDF fitting groups encounter is the presence of tension in data
sets that appear to pull the fits in different directions. In other words, the
best fit depends on the choice of data set. Several methods to capture the
uncertainty in PDFs in presence of seemingly inconsistent fits have been
proposed and are currently in use. These methods are important to ensure that
uncertainty in PDFs are not underestimated. Here we propose a novel method for
estimating the uncertainty by introducing a generalized statistical model
inspired by unsupervised machine learning techniques, namely the Gaussian
Mixture Model (GMM). Using a toy model of PDFs, we demonstrate how the GMM can
be used to faithfully reconstruct the likelihood associated with PDF fits,
which can in turn be used to accurately determine the uncertainty on PDFs,
especially in presence of tension in the fitted data sets. We further show how
this statistical model reduces to the usual chi-squared likelihood function for
a consistent data set and provide measures to optimize the number of Gaussians
in the GMM.
