On fits to correlated and auto-correlated data

Observables in particle physics and specifically lattice QCD calculations are often extracted from fits. Standard $\chi^2$ tests require a reliable determination of the covariance matrix its inverse correlated auto-correlated data, challenging task leading to close-to-singular estimates. These motivate modifications definition such as uncorrelated We show how goodness-of-fit measured by their p-value can still be estimated robustly for broad class