Sequence of seed values for multi-stage random sampling


  • Alias: None

  • Arguments: INTEGERLIST

  • Default: system-generated (non-repeatable)


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.


Defining a multilevel Monte Carlo in the following way

 model_pointer = 'HIERARCH'
   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.