  The quantum Zeno effect freezes the evolution of a quantum system subject to
frequent measure- ments. We apply a Fisher information analysis to show that
because of this effect, a closed quantum system should be probed as rarely as
possible while a dissipative quantum systems should be probed at specifically
determined intervals to yield the optimal estimation of parameters governing
the sys- tem dynamics. With a Bayesian analysis we show that a few frequent
measurements are needed to identify the parameter region within which the
Fisher information analysis applies
