Let us now consider fitting the triplets process to the same data
Figure 1.1 to which we fit the saturation process. We
start with stochastic approximation doing the same as we did with
the saturation process. Start at the Poisson model with parameter
(5.92, 0, 0), making a short run with 
.
Here we are a bit more careful, plotting the 
values over the
course of the run. Values of 
are shown in
Figure 1.3.
Figure 1.3: Time Course of Stochastic Approximation. The stochastic approximation
parameter 
was started at 
. It was lowered to 
at iteration 100 thousand, to 
at 200 thousand, and to 
at
300 thousand.
This run was followed by three more short runs with
values of , , and .
All four runs are shown in the figure.
The lowering of over the course of the runs seems useful.
At the values are all over the lot,
at 
the convergence is very slow.
The parameter values after each of the four short runs shown in Figure 1.3 and a longer run were
We follow this with two MCL steps to obtain an accurate estimate.
In each pair of rows the upper line gives the estimate and the lower gives the Monte Carlo standard error. Our final estimate (4.527, 0.6072, -0.1673) has three to four significant figures of accuracy in the Monte Carlo. The inverse Fisher information is
and the square root of the diagonal elements is (0.15, 0.076, 0.035), which is 100 times the Monte Carlo error.