  Gravitational wave observations of binary neutron star mergers provide
valuable information about neutron star structure and the equation of state of
dense nuclear matter. Numerous methods have been proposed to analyze the
population of observed neutron stars and previous work has demonstrated the
necessity of jointly fitting the astrophysical distribution and the equation of
state in order to accurately constrain the equation of state. In this work, we
introduce a new framework to simultaneously infer the distribution of binary
neutron star masses and the nuclear equation of state using Gaussian mixture
model density estimates which mitigates some of the limitations previously-used
methods suffer from. Using our method, we reproduce previous projections for
the expected precision of our joint mass distribution and equation of state
inference with tens of observations. We also show that mismodeling the equation
of state can bias our inference of the neutron star mass distribution. While we
focus on neutron star masses and matter effects, our method is widely
applicable to population inference problems.
