标题： 从观测数据的扩展贝叶斯分析中双向选择方程组特征得出的典型中子星的经验半径公式 显示英文标题

标题： Empirical radius formulas for canonical neutron stars from bidirectionally selecting EOS features in extended Bayesian analyses of observational data

摘要： 鉴于从引力波和中子星（NS）的X射线观测推断核物质状态方程（EOS）方面取得了显著进展，特别是自GW170817以来，是否存在一种基于数据且稳健的经验公式，能够用特征EOS参数（特征）表示典型NSs的半径$R_{1.4}$？确定$R_{1.4}$的单个最重要但目前尚知之甚少的EOS参数是什么？ 我们通过扩展传统的贝叶斯分析来研究这些问题，传统分析通常以呈现各个EOS参数及其相关性的边缘后验概率分布函数（PDFs）（有时仅呈现皮尔逊相关系数，而这些仅在变量呈线性相关时才可靠有效，而实际上它们往往并非如此）而告终。 利用三种回归模型构建方法：双向逐步特征选择、最小绝对收缩与选择算子（LASSO）回归以及神经网络回归，对大量来自先前全面贝叶斯分析的后验EOS和对应的$R_{1.4}$值进行研究，我们系统且严谨地开发了具有不同统计精度和技术复杂度的最可能的$R_{1.4}$公式。 确定$R_{1.4}$的最重要的 EOS 参数在每次特征/模型选择过程中始终被发现为（按重要性递减顺序）：核对称能量的曲率$K_{sym}$、斜率$L$、核对称能量的偏度$J_{sym}$、对称核物质的偏度$J_{0}$、压缩系数$K_{0}$以及核物质饱和密度$\rho_0$处对称能的大小$E_{sym} (\rho_0)$。 显示英文摘要

摘要： Given the significant advancement in Bayesian inference of nuclear Equation of State (EOS) from gravitational wave and X-ray observations of neutron stars (NSs), especially since GW170817, is there a data-driven and robust empirical formula for the radius $R_{1.4}$ of canonical NSs in terms of the characteristic EOS parameters (features)? What is the single most important but currently poorly known EOS parameter for determining the $R_{1.4}$? We study these questions by extending the traditional Bayesian analysis which normally ends at presenting the marginalized posterior probability distribution functions (PDFs) of individual EOS parameters and their correlations (or sometimes only the Pearson correlation coefficients which are only reliably useful when the variables are linearly correlated while they are actually often not). Using three regression model-building methodologies: bidirectional step-wise feature selection, Least Absolute Shrinkage Selection Operator (LASSO) regression, and neural network regression on a large set of posterior EOSs and the corresponding $R_{1.4}$ values inferred from earlier comprehensive Bayesian analyses of NS observational data, we systematically and rigorously develop the most probable $R_{1.4}$ formulas with varying statistical accuracy and technical complexity. The most important EOS parameters for determining $R_{1.4}$ are found consistently in each of the feature/model selection processes to be (in order of decreasing importance): curvature $K_{sym}$, slope $L$, skewness $J_{sym}$ of nuclear symmetry energy, skewness $J_{0}$, incompressibility $K_{0}$ of symmetric nuclear matter, and the magnitude $E_{sym} (\rho_0)$ of symmetry energy at the saturation density $\rho_0$ of nuclear matter.