To illustrate the method, we choose , and
so that so that
the data will always appear uniformly distributed
when projected on a plane.
Figure 5.8 shows the data as seen from
the plane after 4 and 20 iterations
of the systematic method.
The five facets of the valid region are caused by the manifold
reaching the positivity limit of each of the five dimensions.
Nonuniformity can be clearly seen for 4, but not for 20
iterations.
Figure:
Visual uniformity test for , . The 2D manifold as seen from the
two dimensions after 4 iteration (left)
and 20 iterations (right).

Later, we will discuss the difference between the
systematic and the randomdirections algorithm.
But first, we must solve for the asymptotic mean.
Baggenstoss
20170519