A minimalistic and general weighted averaging method for inconsistent data (2406.08293v2)

Abstract: The weighted average of inconsistent data is a common and tedious problem that many scientists have encountered. The standard weighted average is not recommended for these cases, and different alternative methods are proposed in the literature. Here, we discuss a method first proposed by Sivia in 1996 that is based on Bayesian statistics and keeps the number of assumptions to a minimum. We propose this approach as a new standard for calculating weighted averages. The uncertainty associated with each input value is considered to be just a lower bound of the true unknown uncertainty.The resulting likelihood function is no longer Gaussian, but has smoothly decreasing wings, which allows for a better treatment of scattered data and outliers. The proposed method is tested on a series of data sets: simulations, CODATA recommended value of the Newtonian gravitational constant, and some particle properties from the Particle Data Group, including the proton charge radius. A freely available Python library is also provided for a simple implementation of the proposed averaging method.