  Physical theories that depend on many parameters or are tested against data
from many different experiments pose unique challenges to parameter estimation.
Many models in particle physics, astrophysics and cosmology fall into one or
both of these categories. These issues are often sidestepped with very
simplistic and statistically unsound ad hoc methods, involving naive
intersection of parameter intervals estimated by multiple experiments, and
random or grid sampling of model parameters. Whilst these methods are easy to
apply, they exhibit pathologies even in low-dimensional parameter spaces, and
quickly become problematic to use and interpret in higher dimensions. In this
article we give clear guidance for going beyond these rudimentary procedures,
suggesting some simple methods for performing statistically sound inference,
and recommendations of readily-available software tools and standards that can
assist in doing so. Our aim is to provide physicists with recommendations for
reaching correct scientific conclusions, with only a modest increase in
analysis burden.
