Optimized Statistical Approach for Comparing Multi-messenger Neutron Star Data

The neutron star equation of state 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 often mapped to a common domain for comparison with one another or are used to constrain the predictions of theoretical equations of state. We explore here the statistical biases that can arise when such multi-messenger data are compared or combined across different domains. We find that placing Bayesian priors individually in each domain of measurement can lead to biased constraints. We present a new prescription for defining Bayesian priors consistently across different experiments, which will allow for robust cross-domain comparisons. Using the first two binary neutron star mergers as an example, we show that a uniform prior in the tidal deformability can produce inflated evidence for large radii, while a uniform prior in the radius points toward smaller radii. Finally, using this new prescription, we provide a status update on multi-messenger constraints on the neutron star radius.