On fits to correlated and auto-correlated data

Observables in particle physics and specifically in lattice QCD calculations are often extracted from fits. Standard X2 tests require a reliable determination of the covariance matrix and its inverse from correlated and auto-correlated data, a challenging task often leading to close-to-singular estimates. These motivate modifications of the definition of X2 such as uncorrelated fits. We show how the goodness-of-fit measured by their p-value can still be estimated robustly for a broad class of such fits.(c) 2022 Elsevier B.V. All rights reserved.

Automated summary

Observables in particle physics, particularly in lattice QCD calculations, are often obtained through fits. However, reliable determination of the covariance matrix and its inverse from correlated and auto-correlated data is challenging and can lead to close-to-singular estimates. To address this, modifications of the X2 definition, such as uncorrelated fits, are proposed. We demonstrate how the goodness-of-fit measured by the p-value can still be robustly estimated for a wide range of such fits.