# From Neutron Star Observables to the Equation of State. II. Bayesian Inference of Equation of State Pressures

## TL;DR

This paper develops a Bayesian method to infer neutron star interior pressures at fixed densities from mass-radius data, highlighting the importance of regularization and full posterior analysis for accurate EoS characterization.

## Contribution

It introduces a Bayesian framework for inferring neutron star EoS pressures at fixed densities, accounting for regularization and avoiding biases from marginalization.

## Key findings

- Pressure at twice nuclear saturation density can be inferred within 0.3 dex.
- EoS with phase transitions can be inferred within ~30%.
- Full posterior analysis prevents radius bias of nearly 1 km.

## Abstract

One of the key goals of observing neutron stars is to infer the equation of state (EoS) of the cold, ultradense matter in their interiors. We present here a Bayesian statistical method of inferring the pressures at five fixed densities, from a sample of mock neutron star masses and radii. We show that while five polytropic segments are needed for maximum flexibility in the absence of any prior knowledge of the EoS, regularizers are also necessary to ensure that simple underlying EoS are not over-parametrized. For ideal data with small measurement uncertainties, we show that the pressure at roughly twice the nuclear saturation density, rho_sat, can be inferred to within 0.3 dex for many realizations of potential sources of uncertainties. The pressures of more complicated EoS with significant phase transitions can also be inferred to within ~30%. We also find that marginalizing the multi-dimensional parameter space of pressure to infer a mass-radius relation can lead to biases of nearly 1 km in radius, towards larger radii. Using the full, five-dimensional posterior likelihoods avoids this bias.