  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.
