Asymmetric Uncertainties: Sources, Treatment and Potential Dangers

TL;DR

This paper reviews the origins and implications of asymmetric uncertainties in scientific measurements, highlighting potential biases and providing probabilistic methods for proper treatment.

Contribution

It introduces a comprehensive review of asymmetric uncertainties, analyzes their sources, and offers probabilistic solutions to mitigate bias in reported results.

Findings

Asymmetric uncertainties can bias physical quantity estimates.

Proper probabilistic treatment reduces bias from asymmetric errors.

Published results with asymmetric errors may misrepresent true values.

Abstract

The issue of asymmetric uncertainties resulting from fits, nonlinear propagation and systematic effects is reviewed. It is shown that, in all cases, whenever a published result is given with asymmetric uncertainties, the value of the physical quantity of interest is biased with respect to what would be obtained using at best all experimental and theoretical information that contribute to evaluate the combined uncertainty. The probabilistic solution to the problem is provided both in exact and in approximated forms.