Blurb::
Sequence of seed values for multi-stage random sampling
Description::
This specification allows the stipulation of seed values (passed to a
random number generator) for each of a set of stages within a multi-stage
random sampling algorithm.

This is particularly useful for reusing sample sets (via restart) that
were generated in some other context (e.g., from a single-stage study)
within a multi-stage algorithm execution.  Normally the random number
sequence would continue from a seed specified for the initial sample
set, making subsequent sample sets more difficult to recreate outside
of their original context.  With finer granularity in the seed
specification for multi-stage samplers, intermediate portions of a
sampling sequence can now be more readily recreated and reused.

*Default Behavior*

As for the scalar case, the default is no seed control, such that a
query to a system clock will be used to randomize results.

*Usage Tips*

For $L$ levels in a multilevel method, the ``seed_sequence`` can be of
any length and seeds will be assigned up to the number of values that
are provided or up to the number of levels in the sequence.  Thus, a
seed_sequence of length 1 recovers the behavior of a scalar seed.

When ``fixed_seed`` is unspecified, the ``seed_sequence`` specification
does not extend to the refinement of the sample set.  For example, the
value from the ``seed_sequence`` defines the initial sample set for a
level, but then subsequent sample sets generated as data increments
will allow the random number sequence to continue without resetting
the seed value.  This reflects the need to avoid reusing previous
sample values when generating sample augmentations.
Topics::

Examples::
Defining a multilevel Monte Carlo in the following way

.. code-block::

    method,
     model_pointer = 'HIERARCH'
            multilevel_sampling
       pilot_samples = 100  50   40   30   20
       seed_sequence = 1234 2345 3456 4567 5678

allows the reuse (via restart) of intermediate sample sets from other
sources by matching the seed specifications for the targeted model
resolutions.
Theory::

Faq::

See_Also::
