Response to the following:
Show that the probability of acceptance in an Accept-Reject algorithm with upper bound M on the density ratio f /g is 1/M. Show that the expected value of the acceptance rate, E[I(fˆ /M˜g˜ )], can be used to compute the missing constant in f /g.
As stressed by this exercise, the probability of acceptance is 1/M only if the normalizing constants are known. Otherwise, since the missing constants do get absorbed into M˜ , 1/M˜ is not the probability of acceptance.