Bayesian theory of systematic measurement deviations

TL;DR

This paper introduces a Bayesian approach to properly handle systematic measurement deviations, providing a detailed methodology and practical examples to improve measurement accuracy in scientific experiments.

Contribution

It presents a novel Bayesian framework for correcting systematic measurement deviations, filling a gap in existing guidelines like the GUM.

Findings

Bayesian methods effectively model systematic deviations

The approach improves measurement correction accuracy

Practical examples demonstrate applicability

Abstract

Concerning systematic effects, the recommendation given in the GUM is to correct for them, but unfortunately no detailed information is available, how to do this. This publication will show, how systematic measurement deviations can be handled correctly based on the Bayesian probability theory. After a short overview about useful methods and tools, like the product rule of probability theory, Bayes' theorem, the principle of maximum entropy, and the marginalisation equation, an outline of a method to handle systematic measurement deviations is introduced. Finally some simple examples of practical interest are given, in order to demonstrate the applicability of the suggested method.