Model selection in the average of inconsistent data: an analysis of the measured Planck-constant values

TL;DR

This paper reviews Bayesian methods for selecting the most trustworthy value of a constant from inconsistent measurements, exemplified by estimating the Planck constant.

Contribution

It introduces Bayesian model comparison to address data inconsistency in estimating physical constants, providing a systematic approach for model selection.

Findings

Bayesian inference effectively compares hypotheses about data variance.

Model selection yields a more reliable estimate of the Planck constant.

The approach clarifies the impact of data inconsistency on measurement estimates.

Abstract

When the data do not conform to the hypothesis of a known sampling-variance, the fitting of a constant to a set of measured values is a long debated problem. Given the data, fitting would require to find what measurand value is the most trustworthy. Bayesian inference is here reviewed, to assign probabilities to the possible measurand values. Different hypothesis about the data variance are tested by Bayesian model comparison. Eventually, model selection is exemplified in deriving an estimate of the Planck constant.