Follow a Metropolis random walk that should converge to a beta distribution.  Since the point is
 to have slowly changing probabilities for simulating non-stationary conversion processes, having
 substantial sample to sample correlation is good here.
 
 The probabilities returned will be beta distributed if you take enough steps.  Steps are proposed
 using a normally distributed step in soft-max space which gives a random walk bounded to (0,1) in
 probability space.  The proposal distribution winds up taking very small steps near the
 boundaries with larger steps in the middle.  Steps are accepted or rejected according to the
 Metropolis algorithm.  Computing the probabilities for acceptance or rejection in the probability
 space while taking the step in log-odds space is OK since the proposal probability is still
 symmetrical.