  The increasing richness of data related to cold dense matter, from laboratory
experiments to neutron-star observations, requires a framework for constraining
the properties of such matter that makes use of all relevant information. Here,
we present a rigorous but practical Bayesian approach that can include diverse
evidence, such as nuclear data and the inferred masses, radii, tidal
deformabilities, moments of inertia, and gravitational binding energies of
neutron stars. We emphasize that the full posterior probability distributions
of measurements should be used rather than, as is common, imposing a cut on the
maximum mass or other quantities. Our method can be used with any
parameterization of the equation of state (EOS). We use both a spectral
parameterization and a piecewise polytropic parameterization with variable
transition densities to illustrate the implications of current measurements and
show how future measurements in many domains could improve our understanding of
cold catalyzed matter. We find that different types of measurements will play
distinct roles in constraining the EOS in different density ranges. For
example, better symmetry energy measurements will have a major influence on our
understanding of matter somewhat below nuclear saturation density but little
influence above that density. In contrast, precise radius measurements or
multiple tidal deformability measurements of the quality of those from GW170817
or better will improve our knowledge of the EOS over a broader density range.
