We can easily simulate a realization of the Poisson process, so we start
stochastic approximation in equilibrium with
,
the MLE for the Poisson model, and a simulation
with exactly 372 points uniformly distributed in the unit square. The
starting
was
, a wild guess that happened to work.
Two runs of
and
iterations, taking a total of five and
a half minutes, got close enough to the MLE to switch to MCL methods.
The results of the two runs were.
Whether stochastic approximation does this well in general is an open question. For a bit more difficult example, see Section 1.16