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

Abstract

We discuss the effect of large positive correlations in the combinations of several measurements of a single physical quantity using the Best Linear Unbiased Estimate (BLUE) method. We suggest a new approach for comparing the relative weights of the different measurements in their contributions to the combined knowledge about the unknown parameter, using the well-established concept of Fisher information. We argue, in particular, that one We discuss the effect of large positive correlations in the combinations of several measurements of a single physical quantity using the Best Linear Unbiased Estimate (BLUE) method. We suggest a new approach for comparing the relative weights of the different measurements in their contributions to the combined knowledge about the unknown parameter, using the well-established concept of Fisher information. We argue, in particular, that one contribution to information comes from the collective interplay of the measurements through their correlations and that this contribution cannot be attributed to any of the individual measurements alone. We show that negative coefficients in the BLUE weighted average invariably indicate the presence of a regime of high correlations, where the effect of further increasing some of these correlations is that of reducing the error on the combined estimate. In these regimes, we stress that assuming fully correlated systematic uncertainties is not a truly conservative choice, and that the correlations provided as input to BLUE combinations need to be assessed with extreme care instead. In situations where the precise evaluation of these correlations is impractical, or even impossible, we provide tools to help experimental physicists perform more conservative combinations.

References in corpus (1)

• Electroweak Measurements in Electron-Positron Collisions at W-Boson-Pair Energies at LEP

Cited by in corpus (15)

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• Measurement of the photon identification efficiencies with the ATLAS detector using LHC Run 2 data collected in 2015 and 2016
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• Measurements of the t-tbar production cross section in lepton+jets final states in pp collisions at 8 TeV and ratio of 8 to 7 TeV cross sections
• Production of ${\pi }^0$ and $\eta$ mesons up to high transverse momentum in pp collisions at 2.76 TeV
• Direct photon production at low transverse momentum in proton-proton collisions at $\sqrt{s}$ = 2.76 and 8 TeV
• Measurement of the inclusive $\mathrm{t}\overline{\mathrm{t}}$ cross section in pp collisions at $\sqrt{s}=$ 5.02 TeV using final states with at least one charged lepton
• Neutral pion and $\eta$ meson production at mid-rapidity in Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV
• Measurement of ${\chi }_{c1}(3872)$ production in proton-proton collisions at $\sqrt{s}=8$ and $13$ TeV
• Combinations of single-top-quark production cross-section measurements and $|f_{\mathrm{LV}}{V}_{tb}|$ determinations at $\sqrt{s}=7$ and 8 TeV with the ATLAS and CMS experiments
• Measurement of the inclusive $\mathrm{t}\bar{\mathrm{t}}$ production cross section in proton-proton collisions at $\sqrt{s}=$ 5.02 TeV
• Combination of measurements and the BLUE method
• Production of $\omega$ mesons in pp collisions at $\sqrt{s}$ = 7 TeV
• Measurements of $CP$ asymmetries and branching fraction ratios of $B^{-}$ decays to two charm mesons
• Measurement of $\omega$ meson production in pp collisions at $\sqrt{s}$ = 13 TeV