A Geometric approach to model selection: Application to neutron star equation of state

Astrophysical models map theoretical assumptions into observable predictions through specific parameterizations. Reliable inference from data therefore hinges on priors that provide uniform density and adequate coverage across the resulting model space. If this coverage is uneven or sparse, inferences can be biased by the structure of the prior itself. Existing priors are often chosen heuristically or constrained by computational limits, with no systematic way to quantify the distinguishability between models. We introduce a geometric framework for constructing data-independent, reparameterization-invariant priors. The approach defines a natural metric on model space derived from the expected curvature of the Bayesian evidence. A preset Bayes-factor threshold determines the covering radius, ensuring that all admissible models lie within a specified distance. This framework is particularly well suited to inferring the dense-matter equation of state from multimessenger data, including gravitational waves from binary neutron star mergers, NICER X-ray observations, and other complementary probes. In such applications, where the prior must span the relevant parameter space with uniform fidelity, this geometric construction offers a systematic approach to ensure both completeness and consistency of inference.