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Analysis of data with interval uncertainty: application of a combined sample consistency measure

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Measurement Techniques Aims and scope

Abstract

The article considers one of the main problems of data analysis, i.e., estimation of parameters characterizing the data sample of a constant quantity. Data analysis is required in all areas of experimental physics to obtain reliable measurement results. To describe sample units under bilateral constraints on their error, the apparatus of interval analysis and statistics is used. In particular, data homogeneity in the sample is described using various consistency measures. A set of three consistency measures is presented that describe different relationships between sample units. On the basis of the considered set, a combined sample consistency measure is proposed that can simultaneously provide outer and inner estimates of the quantity under study. The specified estimates are important in solving a massive data processing problem (i.e., processing of a set of samples obtained under different measurement conditions). The article provides necessary information on interval analysis and various interval arithmetics. The relationships between the proposed combined measure and the results of computations with interval twins and fuzzy sets are considered. This combined measure can be used in solving the massive data processing problem typically addressed in theoretical and applied semiconductor physics. A practical example is presented of using the combined sample consistency measure in the testing of solar transducers against a reference transducer as part of the study of their spectral properties and quantum yield.

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Notes

  1. RMG 29-2013. GSI. Metrology. Basic Terms and Definitions.

  2. S. Zhilin. Examples of Interval Data Analysis in Octave [in Russian], collection of Jupyter notebooks with examples of interval data analysis, available at: https://github.com/szhilin/octave-interval-examples (accessed: 10/26/2023).

  3. Solar sensor data and programs for their processing. available at: https://github.com/AlexanderBazhenov/Solar-Data (accessed: 10/31/2023).

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Acknowledgements

The authors are grateful to the participants of the All-Russian Webinar on Interval Analysis: S. Kumkov, A. Prolubnikov, E. Chausova, and S. Sharom for creative and constructive collaboration in the analysis of data with interval uncertainty; V. Nesterov for the discussion of issues related to twin arithmetic; A. Zhavoronkova and T. Iavoruk for the development of twin arithmetic software.

Funding

The work was supported by the Russian Academy of Sciences. The sections “Theoretical Framework of Interval Analysis” and “Measures of Interval Sample Consistency” were prepared under State Contract No. 0034-2019-0001, and the sections “Extreme Parameter Estimates” and “Interval α‑level Parameter Estimates” were prepared under State Contract No. 0040-2019-0023.

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Authors and Affiliations

  1. Ioffe Institute, St. Petersburg, Russian Federation

    A. N. Bazhenov & A. Yu. Telnova

  2. Physics and Mechanics Institute, Peter the Great St. Petersburg Polytechnic University, St. Petersburg, Russian Federation

    A. N. Bazhenov

  3. CSort Ltd, Barnaul, Russian Federation

    S. I. Zhilin

Authors
  1. A. N. Bazhenov
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  2. S. I. Zhilin
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  3. A. Yu. Telnova
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Correspondence to A. N. Bazhenov.

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Translated from Izmeritel’naya Tekhnika, No. 11, pp. 17–25, November 2023. Russian DOI: https://doi.org/10.32446/0368-1025it.2023-11-17-25

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Original article submitted 06/02/2023. Accepted 09/09/2023.

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Bazhenov, A.N., Zhilin, S.I. & Telnova, A.Y. Analysis of data with interval uncertainty: application of a combined sample consistency measure. Meas Tech (2024). https://doi.org/10.1007/s11018-024-02297-y

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  • DOI: https://doi.org/10.1007/s11018-024-02297-y

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