Bob,
Thanks for pointing out that one cannot use NONMEM to describe the
Cauchy distribution. Presumably this explains why we dont seem to have
many physicists on nmusers :-). The normal assumption for NONMEM
simulation seems to be well accepted so no simulated spectral lines I'm
afraid.
However, can you (or anyone) else point out precisely if NONMEM makes
an assumption of normality in its estimation procedure (the answer will
presumably depend on which estimation method is chosen) ?
Juergen suggested the MCPEM flavour of EM requires a normal assumption
for the estimation. But what about SAEM, FOCE, BAYES, etc.?
Nick
Bob Leary wrote:
Nick -
a slight correction. Not all distributions have a variance - the most
familiar and important example
is the Cauchy distribution (1/pi) *1/(1+x^2) - the variance integral
is infinite.
This is actually a significant distribution in physics,
representing the shape of certain spectral
lines. It is also related to the Poisson kernel in solving Laplace
equations.
Bob
------------------------------------------------------------------------
*From:* [email protected] [[email protected]] On
Behalf Of Nick Holford [[email protected]]
*Sent:* Friday, May 28, 2010 2:50 PM
*To:* [email protected]
*Subject:* Re: [NMusers] distribution assumption of Eta in NONMEM
For estimation NONMEM estimates one parameter to describe the
distribution of random effects -- this is the variance (OMEGA) of the
distribution. Thus it makes no explicit assumption that the
distribution is normal. AFAIK any distribution has a variance.
For simulation NONMEM assumes all etas are normally distributed. If
you use OMEGA BLOCK(*) then the distribution is multivariate with
covariances but still normal.
Nick
Ethan Wu wrote:
I could not find in the NONMEM help guide that explicitly mentioned a
normal distribution is assumed, only it was clearly mentioned of
assumption of mean of zero.
------------------------------------------------------------------------
*From:* Serge Guzy <[email protected]>
*To:* Ethan Wu <[email protected]>; [email protected]
*Sent:* Fri, May 28, 2010 1:25:24 PM
*Subject:* RE: [NMusers] distribution assumption of Eta in NONMEM
As far as I know, this is the assumption in most of the population
programs like NONMEM, SADAPT, PDX-MC-PEM and SAEM. Therefore when you
simulate, random values from a normal distribution are generated.
However, you have the flexibility to use any transformation to create
distributions for your model parameters that will depart from pure
normality. For example, CL=theta(1)*exp(eta(1)) will generate a
log-normal distribution for the clearance although the random
deviates are all from the normal distribution.
I am not sure how you can simulate data sets if you are using the non
parametric option that is indeed available in NONMEM.
Serge Guzy; Ph.D
President, CEO, POP_PHARM
www.poppharm.com <http://www.poppharm.com/>
*From:* [email protected]
[mailto:[email protected]] *On Behalf Of *Ethan Wu
*Sent:* Friday, May 28, 2010 9:08 AM
*To:* [email protected]
*Subject:* [NMusers] distribution assumption of Eta in NONMEM
Dear users,
Is it true NONMEM dose not assume Eta a normal distribution?
If it does not, I wonder what distribution it assumes? I guess this
is critical when we do simulations.
Thanks
------------------------------------------------------------------------
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