On the average of inconsistent data

TL;DR

This paper reviews a probabilistic method for fitting a constant to inconsistent data, especially when data uncertainties are uncertain, and applies it to estimate the Planck constant.

Contribution

It introduces a fitting procedure that assigns probabilities based on lower-bound uncertainties and demonstrates its application to fundamental physical constant estimation.

Findings

The method provides a probabilistic estimate of the Planck constant.

It addresses data inconsistency issues in constant fitting.

The approach improves estimation robustness under uncertain measurement errors.

Abstract

When data do not conform to the hypothesis of a known sampling-variance, the fitting of a constant to the set of measured values is a long debated problem. Given the data, the fitting would require to find which measurand value is most probable. A fitting procedure is here reviewed which assigns probabilities to the possible measurand values, on the assumption that the uncertainty associated with each datum is the lower bound to the standard deviation. This procedure is applied to derive an estimate of the Planck constant.