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Stochastic Approximation

We can easily simulate a realization of the Poisson process, so we start stochastic approximation in equilibrium with tex2html_wrap_inline4253 , the MLE for the Poisson model, and a simulation with exactly 372 points uniformly distributed in the unit square. The starting tex2html_wrap_inline2321 was tex2html_wrap_inline2323 , a wild guess that happened to work. Two runs of tex2html_wrap_inline4243 and tex2html_wrap_inline4215 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.

table989

Whether stochastic approximation does this well in general is an open question. For a bit more difficult example, see Section 1.16



Charles Geyer
Fri Jul 5 15:26:21 CDT 1996