Re: RNG

[Rick Riolo]

It seems to me that whether its acceptable
to have the RN sequences overlap over different
runs of an experiment will be model dependent.

For example, if the model is going through some
evolution that is generating new mixes of populations
over the course of the runs, the same (sub)sequence of RNs, 
when it is used at different times in the runs, 
is very unlikely to be used "in the same way," 
i.e., in some way that will introduce undesirable 
correlations across the runs.

of course if the sequences are NOT overlapping,
one doesn't have to worry about whether one's
model will not be adversely affected by sharing
subsequences of RNs at different points in runs,
making such RNG's a goal to shoot for.

 - r

Rick Riolo                       address@hidden
Program for Study of Complex Systems (PSCS)
1061 Randall Lab     University of Michigan
Ann Arbor MI 48109-1120
http://pscs.physics.lsa.umich.edu/PEOPLE/rlr-home.html

On Thu, 27 Mar 1997, Sven N. Thommesen wrote:

> Date: Thu, 27 Mar 1997 19:26:25 -0600
> From: Sven N. Thommesen <address@hidden>
> To: Bob Bell <address@hidden>
> Cc: address@hidden
> Subject: Re: RNG
> 
> At 05:13 PM 3/27/97 -0800, you wrote:
> >
> >hi Sven,
> >
> >Thanks for the help. (and yes, I DID and AM and WILL keep
> >rereading the docs :)  
> >
> >So what is the period of PMMLCG?  I ask since you mentioned
> >the 10e11 for the experiment...but I only need 10e8 for
> >each run. So it seems to me that as long as the period is
> >greater than the random variates used in a SINGLE run
> >I should be OK...would you agree?
> >
> >Thanks again!
> >
> >Bob
> >
> 
> Yes, the first limit is clearly that you don't want a single
> run to 'wrap around' and start the generator over again ...
> So in your case, you may be ok; PMMLCG has a period of
> 2^31-1 (2,147,483,647) or 2.1e9.
> 
> The next limit is for all the numbers needed for a whole 
> experiment (i.e. your 1000 runs) to be statistically 
> independent -- in your case you need something like 1e11
> numbers, so if you use PMMLCG with different starting
> seeds we KNOW that different runs will be using partially 
> overlapping sequences of random numbers. Whether this is 
> acceptable, I don't know; I haven't tested these generators 
> for that.
> 
> The SWB generators have periods of 2^200 (1.6e60) to
> 2^354 (3.66e106), which should be sufficient in your case ...
> Unfortunately, we don't have a way to specify starting
> states that will *guarantee* non-overlapping sequences;
> but the hope is that if you use starting states uniformly
> distributed over the space of possible states, things 
> will be ok. For SWB we use an LCG generator to fill the
> state vector, so giving it seeds uniformly distributed
> over [0,2^32-1] is the best we can do.
> 
> As I mentioned, there's a generator by L'Ecuyer that has a 
> huge period AND a way to 'jump ahead' to get non-
> overlapping sequences; when it's been implemented and
> tested I'll make it available. Provided it tests well,
> it is likely to become the default generator. 
> 
> -Sven
> 
>