On the combination of correlated estimates of a physics observable

Abstract

The combination of a number of correlated estimates of a given observable is frequently performed using the Best Linear Unbiased Estimate ( BLUE ) method. Most features of such a combination can already be seen by analysing the special case of a pair of estimates from two correlated estimators of the observable. Two important parameters of this combination are the weight of the less precise estimate and the ratio of uncertainties of the combined result and the more precise estimate. Derivatives of these quantities are derived with respect to the correlation and the ratio of uncertainties of the two estimates. The impact of using either absolute or relative uncertainties in the BLUE combination is investigated on a number of examples including Peelle’s Pertinent Puzzle. Using an example, a critical assessment is performed of suggested methods to deal with the fact that both the correlation and the ratio of uncertainties of a pair of estimates are typically only known with some uncertainty. Finally, a proposal is made to decide on the usefulness of a combination and to perform it. The proposal is based on possible improvements with respect to the most precise estimate by including additional estimates. This procedure can be applied to the general case of several observables.

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