  We present a methodology for the construction of parton distribution
functions (PDFs) designed to provide an accurate representation of PDF
uncertainties for specific processes or classes of processes with a minimal
number of PDF error sets: specialized minimal PDF sets, or SM-PDFs. We
construct these SM-PDFs in such a way that sets corresponding to different
input processes can be combined without losing information, specifically on
their correlations, and that they are robust upon smooth variations of the
kinematic cuts. The proposed strategy never discards information, so that the
SM-PDF sets can be enlarged by the addition of new processes, until the prior
PDF set is eventually recovered for a large enough set of processes. We
illustrate the method by producing SM-PDFs tailored to Higgs, top quark pair,
and electroweak gauge boson physics, and determine that, when the PDF4LHC15
combined set is used as the prior, around 11, 4 and 11 Hessian eigenvectors
respectively are enough to fully describe the corresponding processes.
