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We discuss the effect of large positive correlations in the combinations ofseveral measurements of a single physical quantity using the Best LinearUnbiased Estimate (BLUE) method. We suggest a new approach for comparing therelative weights of the different measurements in their contributions to thecombined knowledge about the unknown parameter, using the well-establishedconcept of Fisher information. We argue, in particular, that one We discuss theeffect of large positive correlations in the combinations of severalmeasurements of a single physical quantity using the Best Linear UnbiasedEstimate (BLUE) method. We suggest a new approach for comparing the relativeweights of the different measurements in their contributions to the combinedknowledge about the unknown parameter, using the well-established concept ofFisher information. We argue, in particular, that one contribution toinformation comes from the collective interplay of the measurements throughtheir correlations and that this contribution cannot be attributed to any ofthe individual measurements alone. We show that negative coefficients in theBLUE weighted average invariably indicate the presence of a regime of highcorrelations, where the effect of further increasing some of these correlationsis that of reducing the error on the combined estimate. In these regimes, westress that assuming fully correlated systematic uncertainties is not a trulyconservative choice, and that the correlations provided as input to BLUEcombinations need to be assessed with extreme care instead. In situations wherethe precise evaluation of these correlations is impractical, or evenimpossible, we provide tools to help experimental physicists perform moreconservative combinations.

Information and treatment of unknown correlations in the combination of measurements using the BLUE method