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

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 t...

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Detalles Bibliográficos
Autores principales: Valassi, Andrea, Chierici, Roberto
Lenguaje:eng
Publicado: 2013
Materias:
Acceso en línea:https://dx.doi.org/10.1140/epjc/s10052-014-2717-6
http://cds.cern.ch/record/1562050
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author Valassi, Andrea
Chierici, Roberto
author_facet Valassi, Andrea
Chierici, Roberto
author_sort Valassi, Andrea
collection CERN
description 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 the correlations provided as input to BLUE combinations need to be assessed with extreme care. 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.
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spelling cern-15620502023-03-12T04:01:32Zdoi:10.1140/epjc/s10052-014-2717-6http://cds.cern.ch/record/1562050engValassi, AndreaChierici, RobertoInformation and treatment of unknown correlations in the combination of measurements using the BLUE methodParticle Physics - ExperimentWe 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 the correlations provided as input to BLUE combinations need to be assessed with extreme care. 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.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.arXiv:1307.4003CERN-IT-NOTE-2013-003CERN-IT-Note-2013-003oai:cds.cern.ch:15620502013-07-15
spellingShingle Particle Physics - Experiment
Valassi, Andrea
Chierici, Roberto
Information and treatment of unknown correlations in the combination of measurements using the BLUE method
title Information and treatment of unknown correlations in the combination of measurements using the BLUE method
title_full Information and treatment of unknown correlations in the combination of measurements using the BLUE method
title_fullStr Information and treatment of unknown correlations in the combination of measurements using the BLUE method
title_full_unstemmed Information and treatment of unknown correlations in the combination of measurements using the BLUE method
title_short Information and treatment of unknown correlations in the combination of measurements using the BLUE method
title_sort information and treatment of unknown correlations in the combination of measurements using the blue method
topic Particle Physics - Experiment
url https://dx.doi.org/10.1140/epjc/s10052-014-2717-6
http://cds.cern.ch/record/1562050
work_keys_str_mv AT valassiandrea informationandtreatmentofunknowncorrelationsinthecombinationofmeasurementsusingthebluemethod
AT chiericiroberto informationandtreatmentofunknowncorrelationsinthecombinationofmeasurementsusingthebluemethod