  Frequentist and Bayesian phase estimation strategies lead to conceptually
different results on the state of knowledge about the true value of the phase
shift. We compare the two frameworks and their sensitivity bounds to the
estimation of an interferometric phase shift limited by quantum noise,
considering both the cases of a fixed and a fluctuating parameter. We point out
that frequentist precision bounds, such as the Cram\`er-Rao bound, for
instance, do not apply to Bayesian strategies and vice-versa. Similarly, bounds
for fluctuating parameters make no statement about the estimation of a fixed
parameter.
