BONNSAI：贝叶斯方法中的相关恒星观测值
BONNSAI: correlated stellar observables in Bayesian methods
摘要：
在大规模恒星光谱测量和大数据的时代，复杂的统计方法变得越来越重要，以便推断基本的恒星参数，如质量和年龄。贝叶斯技术是一种强大的方法，因为它们可以同时将所有可用的观测值与恒星模型相匹配，同时适当考虑先验知识。然而，在大多数情况下，假设可观测量是不相关的，这通常不是事实。在这里，我们通过将协方差矩阵纳入似然函数，将相关性纳入贝叶斯代码BONSAI。我们推导出的协方差矩阵，除了经典的不确定性，只需要规范的相关参数，描述如何观测协变的参数。我们的相关参数完全取决于方法与观测已确定，并可以在某些情况下解析推导。因此，这种方法的优点是，即使在特定情况下无法获得相关性的信息，但这些信息通常是已知的，也可以说明相关性。由于新的似然模型是一个更好的近似的数据，推断参数的可靠性和鲁棒性提高。我们发现，忽略相关性的偏见推断恒星参数的最有可能的值，并影响这些参数可以确定的精度。例如，我们将我们的技术应用于大质量OB星，但强调它对任何类型的恒星都有效。对于有效温度和表面重力确定的大气模型，我们发现，群众可以低估平均由$0.5σ$和质量的不确定性高估了约2倍时，忽略相关性。与此同时，年龄精度被低估了广泛的恒星参数。[删节]
英文摘要：
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 $0.5σ$ 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]
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