I Stratified sampling based on properties of random number streams

[Stephen Tashi]

TL;DR Summary

Are there techniques to do stratified sampling of simulation outputs by basing the strata on properties of the random number streams involved?

I recall seeing briefing notes dating from about the 1970's that advocated doing stratified sampling of the outputs of simulations by using strata based on properties of the random number streams. However, I don't recall how the strata were to be defined. Is this type of stratified sampling a well known technique?

Futher elaboration: A complicated simulation, such as a combat simulation, usually involves several "random number streams" of pseudo random numbers. Each stream has a designated application. For example one stream might be for the accuracy of "Blue" artillery against "Red" targets. The most natural way to run multiple replications of a simulation is vary the seeds of the random number generators for the streams in a way that the replications can be considered independent. I remember seeing briefing notes that advocated the different technique of doing stratified sampling based on the properties of the random number streams. However, I don't recall what properties of the streams were used to define the strata.

According to the standard theory of stratified sampling, one would have to partition the set of random number streams into mutually exclusive categories and find the probability that an independently generated set of streams would fall into a particular category. Then one would have to run replications of the simulation using each category of streams. How this could be accomplished in practice is an interesting question.

 

[Jarvis323]

The only property I can think of for a stream of random numbers, is the stochastic generating process, or in the simplest case, a probability distribution function as the generator.

I can imagine why you might want to stratify such a stream for a simulation like this, because you might want to ensure that the range of possible conditions is generated consistently. If you didn't stratify, then there would be some chance that your stream is an unlikely one, and if there are multiple streams that go into the same simulation state, then your state space might not be covered very well over a given fixed interval of time.

To stratify streams of random numbers, my guess is you could partition the probability distribution function generating it, sample a batch of numbers that is proportionately within each part, and then shuffle them around before throwing them into the final stream.

If you wanted to stratify the joint streams, then maybe do something similar with a joint distribution.

I think you would find lots of research papers about the topic.