核和中子星中的超卡方运动
Moving Beyond Chi-Squared in Nuclei and Neutron Stars
摘要：
在数据的标准$χ^2$分析中有几个假设，包括经常假设似然函数很好地近似于多元高斯分布。本文简要回顾了标准方法，并描述了如何使用贝叶斯推断来超越似然是高斯的假设。两种不同类型的分析相关的核物理被用作测试用例。第一个是从中子星的质量和半径数据确定致密物质的状态方程。第二个是使用理论核质量模型来拟合现有数据，并预测尚未测量的质量值。对于预测核质量的问题，它表明，近似的似然函数与高斯可以产生偏差的预测未测质量。最后，从这些拟合问题中吸取的教训，提出了一种方法来改善核对称性能量的约束。
英文摘要：
There are several assumptions made in a standard $χ^2$ analysis of data, including the frequent assumption that the likelihood function is well approximated by a multivariate Gaussian distribution. This article briefly reviews the standard approach and describes how Bayesian inference can be used to go beyond the assumption that the likelihood is Gaussian. Two separate types of analysis relevant to nuclear physics are used as test cases. The first is the determination of the equation of state of dense matter from neutron star mass and radius data. The second is the use of theoretical nuclear mass models to fit currently available data and predict the value of masses which have not yet been measured. For the problem of predicting nuclear masses, it is demonstrated that approximating the likelihood function with a Gaussian can produce biased predictions of unmeasured masses. Finally, the lessons learned from these fitting problems are used to propose a method for improving constraints on the nuclear symmetry energy.
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