  The current PDF4LHC recommendation to estimate uncertainties due to parton
distribution functions (PDFs) in theoretical predictions for LHC processes
involves the combination of separate predictions computed using PDF sets from
different groups, each of which comprises a relatively large number of either
Hessian eigenvectors or Monte Carlo (MC) replicas. While many fixed-order and
parton shower programs allow the evaluation of PDF uncertainties for a single
PDF set at no additional CPU cost, this feature is not universal, and moreover
the a posteriori combination of the predictions using at least three different
PDF sets is still required. In this work, we present a strategy for the
statistical combination of individual PDF sets, based on the MC representation
of Hessian sets, followed by a compression algorithm for the reduction of the
number of MC replicas. We illustrate our strategy with the combination and
compression of the recent NNPDF3.0, CT14 and MMHT14 NNLO PDF sets. The
resulting Compressed Monte Carlo PDF (CMC-PDF) sets are validated at the level
of parton luminosities and LHC inclusive cross-sections and differential
distributions. We determine that around 100 replicas provide an adequate
representation of the probability distribution for the original combined PDF
set, suitable for general applications to LHC phenomenology.
