AW: RE: RANMETHOD also for $SIM
Hi Bob and Robert,
I was thinking about VPCs.
My understanding is that if I want to approximate e.g. PI by using pseudo
random numbers. I can count the fraction of random point inside a circle and it
will give me a better approximation for N samples than standard random numbers
would.
Thus I was thinking I could generate VPCs using N=300 pseudo-random samples
which would be as accurate as N=1000 common random numbers. Is there a flaw in
my thinking?
Thanks
Sven
Von: Bob Leary [mailto:[email protected]]
Gesendet: Wednesday, October 10, 2012 06:31 PM
An: Bauer, Robert <[email protected]>; Mensing, Sven;
[email protected] <[email protected]>
Betreff: RE: RANMETHOD also for $SIM
Bob and Sven,
It’s not a question of ‘mathematical correctness’ , but to what use you intend
to put the simulated data. Quasi-random sequences are much different than
pseudo-random sequences and any statistical conclusions you might want to draw
from the simulated data may be dubious. For some purposes such as numerical
integration, quasi-random etas can greatly out perform
pseudo-random etas. But for other purposes, the lack of ‘randomness’ in
quasi-random sequences can make them quite inappropriate. For example,
It is well known that raw (unscrambled) quasi -random sequences cannot be
substituted for pseudo-random sequences in MCMC applications such as SAEM -
results can be
quite nonsensical. Bob’s claim that “„It (use of SOBOL sequnces) would even
be inappropriate (that is, lead to bias) in the SAEM or BAYES method“
is certainly correct for raw SOBOL sequences.
However, scrambling (for example, Owen scrambling given by the S1 option in NM
) may overcome this problem in the MCMC case and currently this is
a research topic of great interest in the MCMC world. For example, Owen and
Tribble
(PNAS , Vol 102, 2005, 8844-8849,
http://www.pnas.org/content/102/25/8844.long) have recently proved that under
some conditions a Metropolis-Hastings algorithm
with quasi-random inputs yields consistent estimates and the method is much
more accurate than ordinary Metroplis-Hastings sampling with standard
pseudo-random inputs.
They also show how to extend the results to Gibbs sampling.
Quoted reply history
From: [email protected] [mailto:[email protected]] On
Behalf Of Bauer, Robert
Sent: Wednesday, October 10, 2012 11:34 AM
To: Mensing, Sven; [email protected]
Subject: [NMusers] RE: RANMETHOD also for $SIM
Sven:
It would be mathematically incorrect to create simulated values using a Sobol
quasi-random method. You would obtain eta and eps values that are not truly
normally distributed. The Sobol technique is specifically designed to improve
the efficiency of Monte Carlo integration in multi-dimensional space, such as
is done during the expectation step of the Monte Carlo importance sampling EM
methods, and for no other purpose. It would even be inappropriate (that is,
lead to bias) in the SAEM or BAYES methods. This is why the Sobol technique is
only for IMP and DIRECT estimation.
Robert J. Bauer, Ph.D.
Vice President, Pharmacometrics, R&D
ICON Development Solutions
7740 Milestone Parkway
Suite 150
Hanover, MD 21076
Tel: (215) 616-6428
Mob: (925) 286-0769
Email: [email protected]<mailto:[email protected]>
Web: http://www.iconplc.com/
________________________________
From: [email protected]<mailto:[email protected]>
[mailto:[email protected]]<mailto:[mailto:[email protected]]>
On Behalf Of Mensing, Sven
Sent: Wednesday, October 10, 2012 8:57 AM
To: [email protected]<mailto:[email protected]>
Subject: [NMusers] RANMETHOD also for $SIM
Hello,
is it possible to use the Sobol pseudo-random number generator (e.g.
RANMETHOD=2S) for $SIMULATION problems? Maybe in NM 7.3?
Thanks
Sven
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