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.