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Observables in particle physics and specifically in lattice QCD calculationsare often extracted from fits. Standard $\chi^2$ tests require a reliabledetermination of the covariance matrix and its inverse from correlated andauto-correlated data, a challenging task often leading to close-to-singularestimates. These motivate modifications of the definition of $\chi^2$ such asuncorrelated fits. We show how the goodness-of-fit measured by their p-valuecan still be estimated robustly for a broad class of such fits.

On fits to correlated and auto-correlated data