is a generative model.
To generate from
, we modify
the method in Section 2.2.2 slightly.
is most easily
thought of as a two-step process 
The above process seems overly simple, but this is deceptive,
as we will later see. Not only can the second step be diffiicult, but the
process generates remarkably complex distributions.
- Draw a sample from the feature density
This sample is denoted by .
- Determine the manifold
and draw a sample
from the manifold using the uniform distribution.
We call this uniform manifold sampling (UMS).
Note that one must be careful to insure that, when the manifold is
parameterized, for example with angle, that the uniform distribution
must be imposed in , which does not necessarily mean
that the parameters will be uniformly distributed.