  In this paper we describe the Bayesian link between the cosmological mass
function and the distribution of times at which isolated halos of a given mass
exist. By assuming that clumps of dark matter undergo monotonic growth on the
time-scales of interest, this distribution of times is also the distribution of
`creation' times of the halos. This monotonic growth is an inevitable aspect of
gravitational instability. The spherical top-hat collapse model is used to
estimate the rate at which clumps of dark matter collapse. This gives the prior
for the creation time given no information about halo mass. Applying Bayes'
theorem then allows any mass function to be converted into a distribution of
times at which halos of a given mass are created. This general result covers
both Gaussian and non-Gaussian models. We also demonstrate how the mass
function and the creation time distribution can be combined to give a joint
density function, and discuss the relation between the time distribution of
major merger events and the formula calculated. Finally, we determine the
creation time of halos within three N-body simulations, and compare the link
between the mass function and creation rate with the analytic theory.

Astrophysics