An objective theory of phase shift estimation is formulated within qua
ntum mechanics and quantum estimation theory. The general validity of
Bayesian analysis even in the limit of very low particle numbers is de
monstrated using the information of measured phase-sensitive data. The
formalism was applied to the estimation of an unknown phase in neutro
n interferometry operating near the quantum limit, when only a few par
ticles are registered, and also in the regime of large particle number
s.