To see the effect of dimension on the
as predictor of the asymptotic mean of MCMC-UMS,
we repeated the experiment of Figure 5.12
for various manifold dimensions .
In Figure 5.13, we plotted
after 20,000 full iterations of MCMC-UMS
(systematic approach and whitening).
Plotted is the average of for three trials
at each dimension.
We see that even for manifold dimension 3, there is
good accuracy. Note that
that the fractional error has a standard deviation of
.055 or 5.5% error. At a dimension of 125,
is about .00009, a fractional error
standard deviation of 1%.
Mean square fractional error
as a function of dimension estimated using 20,000 iterations.