  One of the key goals of observing neutron stars is to infer the equation of
state (EoS) of the cold, ultradense matter in their interiors. We present here
a Bayesian statistical method of inferring the pressures at five fixed
densities, from a sample of mock neutron star masses and radii. We show that
while five polytropic segments are needed for maximum flexibility in the
absence of any prior knowledge of the EoS, regularizers are also necessary to
ensure that simple underlying EoS are not over-parametrized. For ideal data
with small measurement uncertainties, we show that the pressure at roughly
twice the nuclear saturation density, rho_sat, can be inferred to within 0.3
dex for many realizations of potential sources of uncertainties. The pressures
of more complicated EoS with significant phase transitions can also be inferred
to within ~30%. We also find that marginalizing the multi-dimensional parameter
space of pressure to infer a mass-radius relation can lead to biases of nearly
1 km in radius, towards larger radii. Using the full, five-dimensional
posterior likelihoods avoids this bias.
