  Understanding the dense matter equation of state at extreme conditions is an
important open problem. Astrophysical observations of neutron stars promise to
solve this, with NICER poised to make precision measurements of mass and radius
for several stars using the waveform modelling technique. What has been less
clear, however, is how these mass-radius measurements might translate into
equation of state constraints and what are the associated equation of state
sensitivities. We use Bayesian inference to explore and contrast the
constraints that would result from different choices for the equation of state
parametrization; comparing the well-established piecewise polytropic
parametrization to one based on physically motivated assumptions for the speed
of sound in dense matter. We also compare the constraints resulting from
Bayesian inference to those from simple compatibility cuts. We find that the
choice of equation of state parametrization and particularly its prior
assumptions can have a significant effect on the inferred global mass-radius
relation and the equation of state constraints. Our results point to important
sensitivities when inferring neutron star and dense matter properties. This
applies also to inferences from gravitational wave observations.
