We may improve mixing even further by ``whitening" the
Since we have verified that
we can now predict the mean of the MCMC-UMS procedure
and can transform the problem.
be the ``whitened" raw input spectrum,
the compensated matrix
which obtains the same feature
The new linear constraint ``manifold" is:
As a starting vector for
, we can use the
vector of ones, denoted by , since clearly
The MCMC-UMS procedure, then should produce random spectral vectors
that have approximate mean and meet (5.25).
These random vectors can be transformed
to produce solutions to the original problem
The vectors produced this way are actually
random samples for the original problem
because they are in
and the linear whitening operation preserves the uniform distribution.
The result of whitening can be seen in Figure 5.12
and the result is dramatic. The change in ESS
(seen by drawing a horizontal line)
and is more than an order of magnitude
for both systematic and random directions.