  Homogeneous melting of superheated crystals at constant energy is a dynamical
process, believed to be triggered by the accumulation of thermal vacancies and
their self-diffusion. From microcanonical simulations we know that if an ideal
crystal is prepared at a given kinetic energy, it takes a random time $t_w$
until the melting mechanism is actually triggered. In this work we have studied
in detail the statistics of $t_w$ for melting at different energies by
performing a large number of Z-method simulations and applying state-of-the-art
methods of Bayesian statistical inference. By focusing on the short-time tail
of the distribution function, we show that $t_w$ is actually gamma-distributed
rather than exponential (as asserted in previous work), with decreasing
probability near $t_w \sim 0$. We also explicitly incorporate in our model the
unavoidable truncation of the distribution function due to the limited total
time span of a Z method simulation. The probabilistic model presented in this
work can provide some insight into the dynamical nature of the homogeneous
melting process, as well as giving a well-defined practical procedure to
incorporate melting times from simulation into the Z-method in order to reduce
the uncertainty in the melting temperature.
