Hyper-Fit：使用多元高斯不确定性拟合多维数据的线性模型
Hyper-Fit: Fitting Linear Models to Multidimensional Data with Multivariate Gaussian Uncertainties
摘要：
天文数据通常是不确定的，误差是异方差的（每个数据点都不同），不同维度之间的协变。假设一组D维数据点可以用一个具有内在散射的（D - 1）维平面来描述，我们推导出要最大化的一般似然函数，以恢复最佳拟合模型。除了数学描述，我们还发布了R统计语言的hyper-fit包（hyper.fit）和用于在线拟合的用户友好的Web界面（hyperfit.icrar.org）。Hyper-fit套装提供了大量的拟合程序，包括可视化工具，并在广泛的用户手册中有完整的记录。大部分的hyper-fit功能都可以通过Web界面访问。在本文中，我们包括应用玩具的例子和真正的天文数据从文献中：质量大小，塔利费舍尔，基本平面，质量自旋形态关系。在大多数情况下，超拟合解决方案与公布的值非常一致，但揭示了有关拟合模型的更多信息。
英文摘要：
Astronomical data is often uncertain with errors that are heteroscedastic (different for each data point) and covariant between different dimensions. Assuming that a set of D-dimensional data points can be described by a (D - 1)-dimensional plane with intrinsic scatter, we derive the general likelihood function to be maximised to recover the best fitting model. Alongside the mathematical description, we also release the hyper-fit package for the R statistical language (github.com/asgr/hyper.fit) and a user-friendly web interface for online fitting (hyperfit.icrar.org). The hyper-fit package offers access to a large number of fitting routines, includes visualisation tools, and is fully documented in an extensive user manual. Most of the hyper-fit functionality is accessible via the web interface. In this paper we include applications to toy examples and to real astronomical data from the literature: the mass-size, Tully-Fisher, Fundamental Plane, and mass-spin-morphology relations. In most cases the hyper-fit solutions are in good agreement with published values, but uncover more information regarding the fitted model.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
