RE: Re[2]: Covariance: Matrix=S or Matrix=R
From: "Stephen Duffull" sduffull@pharmacy.uq.edu.au
Subject: RE: Re[2]: [NMusers] Covariance: Matrix=S or Matrix=R
Date: Fri, 16 Sep 2005 08:49:23 +1000
Hi Mark
Thanks for your email. You make your argument very clear and conceptually I
agree completely. You wrote in your last comment:
>> I think the text is unclear, the R and S matrix tell you
>> nothing about whether this is a local or global minima, only
>> if it is a minima (or either kind) or a saddle point.
To relate this to the original question which I believe related to the idea
that the R matrix is more sensitive to saddle points compared to the S
matrix. Now without my NONMEM manuals at hand I risk making some frightful
mistakes (but someone will correct me, I'm sure). The R matrix (I think)
most closely relates to the Hessian. The S matrix is an asymptotic result
for the R matrix (I am sure someone who has a manual with them will comment
here). For all intents and purposes S should be pretty similar to R and
therefore also to the "sandwich" matrix reported by NONMEM in $COV which is
akin to the weighted average of the R and S matrices. Therefore I am not
convinced that there is much between the R and S matrices in terms of what
they tell you, which is similar to what you have suggested above, other than
the R matrix is more difficult to compute.
i.e. I am not convinced that R tells you more about saddle points than S.
Does anyone have any more specific beliefs about R and S?
Steve
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Stephen Duffull
School of Pharmacy, University of Queensland, Brisbane 4072, Australia
Tel +61 7 3365 8808, Fax +61 7 3365 1688, Email: sduffull@pharmacy.uq.edu.au
www http://www.uq.edu.au/pharmacy/index.html?page=31309
Design: http://www.uq.edu.au/pharmacy/sduffull/POPT.htm
MCMC: http://www.uq.edu.au/pharmacy/sduffull/MCMC_eg.htm
University Provider Number: 00025B
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