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

TL;DR

This paper examines how large positive correlations affect measurement combinations using the BLUE method, proposing a Fisher information-based approach to better understand the contributions and emphasizing careful assessment of correlations.

Contribution

It introduces a Fisher information-based framework to analyze the impact of correlations in BLUE combinations and provides tools for more conservative estimates when correlations are uncertain.

Findings

Negative BLUE coefficients indicate high correlation regimes.

Increasing correlations can reduce the combined estimate error.

Assuming fully correlated uncertainties is often not conservative.

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.