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Gravitational wave observations of binary neutron star mergers providevaluable information about neutron star structure and the equation of state ofdense nuclear matter. Numerous methods have been proposed to analyze thepopulation of observed neutron stars and previous work has demonstrated thenecessity of jointly fitting the astrophysical distribution and the equation ofstate in order to accurately constrain the equation of state. In this work, weintroduce a new framework to simultaneously infer the distribution of binaryneutron star masses and the nuclear equation of state using Gaussian mixturemodel density estimates which mitigates some of the limitations previously-usedmethods suffer from. Using our method, we reproduce previous projections forthe expected precision of our joint mass distribution and equation of stateinference with tens of observations. We also show that mismodeling the equationof state can bias our inference of the neutron star mass distribution. While wefocus on neutron star masses and matter effects, our method is widelyapplicable to population inference problems.

Hierarchical Inference of Binary Neutron Star Mass Distribution and Equation of State with Gravitational Waves