Optimized statistical approach for combining multi-messenger data for neutron star equation of state inference.

The neutron star equation of state (EOS) is now being constrained from a diverse set of multi-messenger data, including gravitational waves from binary neutron star mergers, X-ray observations of the neutron star radius, and many types of laboratory nuclear experiments. These measurements are typically mapped to a common domain -- either to a corresponding radius or to a parametrized EOS using a Bayesian inference scheme -- for comparison with one another. We explore here the statistical biases that can arise when such multi-messenger data are mapped to a common domain for comparison. We find that placing Bayesian priors individually in each domain of measurement can transform to biased constraints in the domain of comparison. Using the first two binary neutron star mergers as an example, we show that a uniform prior in the tidal deformability can produce artificial evidence for large radii, which the data do not support. We present a new prescription for defining Bayesian priors in any domain of measurement, that will allow for minimally-biased constraints in the domain of comparison. Finally, using this new prescription, we provide a status update on multi-messenger EOS constraints on the neutron star radius.