Use of Bayesian statistics to reduce the density shift uncertainty in Cesium fountain

In this paper Bayesian analysis is applied to a Cesium fountain frequency standard to estimate the density shift correction, the maser drift and their uncertainty as well. Cesium fountain frequency standards realize the second in the International System of Units with a relative uncertainty approaching 10^-16. Among the main contributions to the accuracy budget, cold collisions play an important role because of the so called atomic density shift of the reference atomic transition. The Bayes theorem allows the a priori knowledge of the sign of the collision shift, that is definitively negative, to be rigorously embedded into the analysis; also the magnitude of the maser drift is known from previous results. We analyze the effect of the Bayesian approach on seven different frequency evaluation of a Maser frequency reported to the BIPM from 2008 to 2010 using IT-CsF1. Comparing the results obtained with the two statistics it is evident a 35% reduction of the frequency uncertainty of the maser frequency estimate, in favour of the Bayesian approach.