Uncertainty and auto-correlation in Measurement

TL;DR

This paper explores the reasons behind measurement scatter despite deterministic models, and presents methods to calculate uncertainty and best estimates considering auto-correlations in experimental data.

Contribution

It introduces a detailed analysis of measurement uncertainty and proposes a method to incorporate auto-correlation effects into uncertainty estimation.

Findings

Measurement scatter arises from inherent fluctuations in real-world experiments.

A method to calculate uncertainty of individual observations is presented.

Auto-correlation effects are shown to influence the estimation of the best measurement value.

Abstract

Although a system is described by a well-known set of equations leading to a deterministic behavior, in the real world the value of a measurand obtained by an experiment will mostly scatter. Accordingly, an uncertainty is associated with that value of the measurand due to apparently random fluctuation. This papers deals with the question why this discrepancy exist. Furthermore it will be shown how the uncertainty of one individual observation is calculated and consequently how the best estimate and its corresponding uncertainty considerering auto-correlstions is determined.