  We show that there exists a large class of regularization schemes for
probabilistic predictions in the theory of a self-reproducing inflationary
univere, all of which eliminate the apparent dependence on the time
reparametrization. However, all these schemes lead to different answers for
relative probabilities of finding various types of post-inflationary universes.
Besides, all these schemes fail to be reparametrization invariant beyond the
range of the inflaton field close to end of inflation boundary. Therefore, we
argue that at the current level of understanding, the simple regularization
schemes associated with cutoffs at equal time hypersurfaces are as good as the
recently proposed more complicated procedures which try to fix the
time-reparametrization dependence.
