Statistics of Measuring Neutron Star Radii: Assessing A Frequentist and A Bayesian Approach

TL;DR

This paper compares frequentist and Bayesian methods for measuring neutron star radii, finding Bayesian approaches reduce bias and better account for uncertainties, improving the reliability of such measurements.

Contribution

It introduces a Bayesian framework for neutron star radius estimation and compares it with the traditional frequentist approach, highlighting advantages in bias reduction.

Findings

Frequentist approach exhibits biases larger than required accuracy.

Bayesian method yields larger but less biased uncertainties.

Careful systematic uncertainty assessment removes the need for ad hoc biases.

Abstract

Measuring neutron star radii with spectroscopic and timing techniques relies on the combination of multiple observables to break the degeneracies between the mass and radius introduced by general relativistic effects. Here, we explore a previously used frequentist and a newly proposed Bayesian framework to obtain the most likely value and the uncertainty in such a measurement. We find that, for the expected range of masses and radii and for realistic measurement errors, the frequentist approach suffers from biases that are larger than the accuracy in the radius measurement required to distinguish between the different equations of state. In contrast, in the Bayesian framework, the inferred uncertainties are larger, but the most likely values do not suffer from such biases. We also investigate ways of quantifying the degree of consistency between different spectroscopic measurements from a single source. We show that a careful assessment of the systematic uncertainties in the measurements eliminates the need for introducing ad hoc biases, which lead to artificially large inferred radii.