Uncertainties due to imperfect knowledge of systematic effects: general considerations and approximate formulae

TL;DR

This paper discusses how to properly account for uncertainties in experimental results, especially systematic effects, using Bayesian methods and provides practical formulas for uncertainty propagation.

Contribution

It introduces a Bayesian framework for uncertainty propagation that includes systematic effects and derives approximate formulas for moments of the probability distribution.

Findings

Bayesian approach allows consistent inclusion of all uncertainty sources.

Derived practical formulas for first moments up to second-order approximations.

Provides a general methodology for handling asymmetric uncertainty intervals.

Abstract

Starting from considerations about meaning and subsequent use of asymmetric uncertainty intervals of experimental results, we review the issue of uncertainty propagation. We show that, using a probabilistic approach (the so-called Bayesian approach), all sources of uncertainty can be included in a logically consistent way. Practical formulae for the first moments of the probability distribution are derived up to second-order approximations.