Hyper-Fit: Fitting Linear Models to Multidimensional Data with Multivariate Gaussian Uncertainties

Abstract

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.