Bayesian inference of a negative quantity from positive measurement results

TL;DR

This paper applies Bayesian analysis to estimate the probability distribution of a quantity with a known sign from measurement results, demonstrating advantages over classical methods in atomic clock calibration.

Contribution

It introduces a Bayesian approach for inferring the sign and value of a quantity from positive measurements, improving accuracy in atomic clock applications.

Findings

Bayesian analysis provides a consistent probability density for the quantity.

The method improves estimation of atom density shifts in cesium fountain clocks.

Comparison shows advantages over classical statistical analysis.

Abstract

In this paper the Bayesian analysis is applied to assign a probability density to the value of a quantity having a definite sign. This analysis is logically consistent with the results, positive or negative, of repeated measurements. Results are used to estimate the atom density shift in a caesium fountain clock. The comparison with the classical statistical analysis is also reported and the advantages of the Bayesian approach for the realization of the time unit are discussed.