On fits to correlated and auto-correlated data

Abstract

Observables in particle physics and specifically in lattice QCD calculations are often extracted from fits. Standard ${\chi }^2$ 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 ${\chi }^2$ 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.

arXiv comment15 pages, 4 figures, matching published version

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Cited by in corpus (6)

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• Precision lattice calculation of the hadronic contribution to the running of the electroweak gauge couplings
• Application of Laplace filters to the analysis of lattice time correlators
• Harnessing finite-size effects to gauge aging in the $2D$ Ising model
• $f_K/f_{\pi }$ in iso-symmetric QCD and the CKM matrix unitarity