BONNSAI: correlated stellar observables in Bayesian methods

TL;DR

This paper introduces an improved Bayesian method, BONNSAI, that incorporates correlations between stellar observables using a covariance matrix, leading to more accurate and reliable stellar parameter estimations.

Contribution

It develops a new parametrization of the covariance matrix for Bayesian inference, accounting for correlations even with limited information, enhancing the robustness of stellar parameter estimation.

Findings

Neglecting correlations biases stellar parameter estimates.

Including correlations improves the accuracy of mass and age determinations.

Masses can be underestimated by 0.5σ when ignoring correlations.

Abstract

In an era of large spectroscopic surveys of stars and big data, sophisticated statistical methods become more and more important in order to infer fundamental stellar parameters such as mass and age. Bayesian techniques are powerful methods because they can match all available observables simultaneously to stellar models while taking prior knowledge properly into account. However, in most cases it is assumed that observables are uncorrelated which is generally not the case. Here, we include correlations in the Bayesian code BONNSAI by incorporating the covariance matrix in the likelihood function. We derive a parametrisation of the covariance matrix that, in addition to classical uncertainties, only requires the specification of a correlation parameter that describes how observables co-vary. Our correlation parameter depends purely on the method with which observables have been determined and can be analytically derived in some cases. This approach therefore has the advantage that correlations can be accounted for even if information for them are not available in specific cases but are known in general. Because the new likelihood model is a better approximation of the data, the reliability and robustness of the inferred parameters are improved. We find that neglecting correlations biases the most likely values of inferred stellar parameters and affects the precision with which these parameters can be determined. For example, we apply our technique to massive OB stars, but emphasise that it is valid for any type of stars. For effective temperatures and surface gravities determined from atmosphere modelling, we find that masses can be underestimated on average by $0.5\sigma$ and mass uncertainties overestimated by a factor of about 2 when neglecting correlations. At the same time, the age precisions are underestimated over a wide range of stellar parameters. [abridged]