  Monte Carlo (MC) simulations are extensively used for various purposes in
modern high-energy physics (HEP) experiments. Precision measurements of
established Standard Model processes or searches for new physics often require
the collection of vast amounts of data. It is often difficult to produce MC
samples containing an adequate number of events to allow for a meaningful
comparison with the data, as substantial computing resources are required to
produce and store such samples. One solution often employed when producing MC
samples for HEP experiments is to partition the phase space of particle
interactions into multiple regions and produce the MC samples separately for
each region. This approach allows to adapt the size of the MC samples to the
needs of physics analyses that are performed in these regions. In this paper we
present a procedure for combining MC samples that overlap in phase space. The
procedure is based on applying suitably chosen weights to the simulated events.
We refer to the procedure as "stitching". The paper includes different examples
for applying the procedure to simulated proton-proton collisions at the CERN
Large Hadron Collider.
