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Bayesian model selection: Application to adjustment of fundamental physical constants

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Abstract

The location-scale model is usually present in physics and chemistry in connection to the Birge ratio method for the adjustment of fundamental physical constants such as the Planck constant or the Newtonian constant of gravitation, while the random effects model is the commonly used approach for meta-analysis in medicine. These two competitive models are used to increase the quoted uncertainties of the measurement results to make them consistent. The intrinsic Bayes factor (IBF) is derived for the comparison of the random effects model to the location-scale model, and we answer the question which model performs better for the determination of the Newtonian constant of gravitation. The results of the empirical illustration support the application of the Birge ratio method which is currently used in the adjustment of the CODATA 2018 value for the Newtonian constant of gravitation together with its uncertainty. The results of the simulation study illustrate that the suggested procedure for model selection is decisive even when data consist of a few measurement results.

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  • Bodnar, Olha & Eriksson, Viktor, 2021. "Bayesian model selection: Application to adjustment of fundamental physical constants," Working Papers 2021:7, Örebro University, School of Business.
    • Handle: RePEc:hhs:oruesi:2021_007
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    2. S. Alighanbari & G. S. Giri & F. L. Constantin & V. I. Korobov & S. Schiller, 2020. "Precise test of quantum electrodynamics and determination of fundamental constants with HD+ ions," Nature, Nature, vol. 581(7807), pages 152-158, May.
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    4. Fernández, Carmen & Steel, Mark F. J., 1999. "Reference priors for the general location-scale modelm," Statistics & Probability Letters, Elsevier, vol. 43(4), pages 377-384, July.
    5. A. E. Ades & G. Lu & J. P. T. Higgins, 2005. "The Interpretation of Random-Effects Meta-Analysis in Decision Models," Medical Decision Making, , vol. 25(6), pages 646-654, November.
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    1. Bodnar, Olha, 2021. "Bayesian Model Selection for Small Datasets of Measurement Results," Working Papers 2021:6, Örebro University, School of Business.

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    More about this item

    Keywords

    Intrinsic Bayes factor; Birge ratio method; Location-scale model; Random-e ects model; Reference prior; Meta-analysis; Interlaboratory comparison study; Newtonian constant of gravitation;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General

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