Finding Universal Relations using Statistical Data Analysis

TL;DR

This paper applies statistical data analysis techniques to identify and evaluate universal relations among neutron star features, introducing novel multivariate relations with improved accuracy for astrophysical modeling.

Contribution

It demonstrates the use of correlation measures and multivariate statistics to find and validate EoS independent relations among neutron star features, including new multivariate relations.

Findings

Distance Correlation and Mutual Information effectively identify universal feature pairs.

Multivariate analysis yields a new relation for neutron star $f$-mode frequency with reduced error.

Proposed relations outperform existing bivariate models in accuracy.

Abstract

We present applications of statistical data analysis methods from both bi- and multivariate statistics to find suitable sets of neutron star features that can be leveraged for accurate and EoS independent -- or universal -- relations. To this end, we investigate the ability of various correlation measures such as Distance Correlation and Mutual Information in identifying universally related pairs of neutron star features. We also evaluate relations produced by methods of multivariate statistics such as Principal Component Analysis to assess their suitability for producing universal relations with multiple independent variables. As part of our analyses, we also put forward multiple entirely novel relations, including a multivariate relation for the $f$-mode frequency of neutron stars with a reduced average relative error of $0.010$, compared to an error of $0.015$ of existing, bivariate relations.