Fast Bayesian Updating of the Neutron-Star Equation of State with Neural Posterior and Evidence Estimation

Abstract

We present two complementary neural routes for microscopic neutron-star EOS inference: truncated sequential neural posterior estimation with mixture importance sampling (TSNPE+MIS), which targets one observation, and amortized neural posterior estimation with importance sampling (A-NET+IS), which is reused across nuclear inputs and NICER sources. Both are corrected against the original prior and full likelihood, with the effective sample size as a diagnostic. We test nucleonic and hyperonic relativistic mean-field models with nuclear data, NICER, GW170817, and pQCD. For the fiducial analyses, both agree with UltraNest in the parameter posteriors and 90% mass-radius and tidal-deformability bands. TSNPE+MIS band-edge differences are only 0.024-0.033 km and 1.02-1.03%, while A-NET+IS differences are 0.019-0.050 km and 0.86-1.13%. TSNPE+MIS reduces the computing time by factors of 1.6-2.3; after training, A-NET+IS is 15-240 times faster per configuration. The frozen A-NET also analyzes three NICER sources absent from training, including the newly reported high-mass, compact PSR J1614-2230 posterior. For this source, the inferred $R_{1.4}$ agrees with UltraNest within 0.010 km for nucleonic matter and 0.009 km for hyperonic matter. We also introduce a Green-function Evidence Network (EN), a regression-based variant of Evidence Networks and, to our knowledge, the first Evidence Network applied to neutron-star EOS inference. After a one-time cost, its network queries return absolute evidences in about 0.03 s for new nuclear data and 3.5 s for a new NICER source; all 16 differences from UltraNest are below $1\sigma$, and independent importance-sampling evidences agree within the quoted EN uncertainties. Under the adopted likelihood, both evidence calculations favor nucleonic matter by Bayes factors of about 22:1-27:1.