A Theory of Measurement Uncertainty Based on Conditional Probability

TL;DR

This paper develops a comprehensive Bayesian-based theory of measurement uncertainty that applies broadly, unifying existing standards as a special case when linear approximations are valid.

Contribution

It introduces a general Bayesian framework for measurement uncertainty, extending ISO standards to more complex, nonlinear measurement scenarios.

Findings

Reproduces ISO measurement uncertainty as a special case

Provides a Bayesian approach applicable to complex measurement problems

Unifies various measurement uncertainty concepts under a single theoretical framework

Abstract

A theory of measurement uncertainty is presented, which, since it is based exclusively on the Bayesian approach and on the subjective concept of conditional probability, is applicable in the most general cases. The recent International Organization for Standardization (ISO) recommendation on measurement uncertainty is reobtained as the limit case in which linearization is meaningful and one is interested only in the best estimates of the quantities and in their variances.