  The wide range of sub- and super-nuclear densities achieved in neutron stars
makes them ideal probes of dense nuclear behavior in the form of the nuclear
equation of state (EoS). Studying neutron stars both in isolation and in highly
dynamic events, many recent observations, most famously the gravitational wave
and electromagnetic signals associated with the BNS merger GW170817/AT2017gfo,
have provided suggestive insight into these highest nuclear densities.
Measurements of galactic neutron star masses and radii from NICER and other
radio and X-ray measurements provide critical complementary perspectives,
bounding other features of the EoS. Though nominally congruent, in this paper
we highlight many underappreciated "hidden" priors embedded in joint analysis
of these many messengers, and their systematic impact on joint EoS inference.
In this work, we perform a careful step-by-step Bayesian inference using a
simple low-dimensional parametric EoS model, incrementally adding information
from galactic pulsars, gravitational wave sources, and more speculative
constraints involving kilonovae and the neutron star maximum mass. At each
stage, we carefully discuss the marginal likelihood, explaining how hidden
priors impact conclusions. Conversely, we also quantify how much information
these measurements have, arguing that many if not most have minimal impact
relative to the explicit and hidden prior assumptions. Specifically, we find
two features dominate our inference: on the one hand, the choice of EoS
parameterization and particularly hyperprior, and on the other the
astrophysical priors associated with interpreting events, particularly the
multimessenger source GW170817. In an appendix, we outline a simple
semianalytic projection suitable for assessing the measurability of the EoS
with ensembles of present and future detections.
