Bayesian model selection: Application to adjustment of fundamental physical constants

TL;DR

This paper compares two statistical models, the location-scale and random effects models, for adjusting fundamental physical constants, using Bayesian methods to determine which model performs better, with application to the Newtonian constant of gravitation.

Contribution

It derives the intrinsic Bayes factor for model comparison and demonstrates its effectiveness in selecting the appropriate model for physical constant adjustment.

Findings

Support for the Birge ratio method in CODATA 2018 adjustments

Bayesian model selection is effective even with few measurements

The location-scale model performs better for the Newtonian constant of gravitation

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.