RE: $PRIOR with normal for OMEGA?
Hi Mark,
As I’m sure you know NONMEM has the TNPRI functionality for that. If you want
to use it without the TNPRI functionality, you can estimate OMEGA as THETA and
use a multivariate normal for that. If you have off-diagonal elements, you may
want to do a Cholesky transformation (you can get that automatically in PsN).
As Andy writes there are pros and cons with different priors. While IW has a
better shape to its prior for variances, it is problematic that there is no
correlation between the typical value estimates and their variances.
Best regards,
Mats
Mats Karlsson, PhD
Professor of Pharmacometrics
Dept of Pharmaceutical Biosciences
Faculty of Pharmacy
Uppsala University
Box 591
75124 Uppsala
Phone: +46 18 4714105
Fax + 46 18 4714003
http://www.farmbio.uu.se/research/researchgroups/pharmacometrics/
Quoted reply history
From: [email protected] [mailto:[email protected]] On
Behalf Of Gewitz, Andrew
Sent: Friday, November 11, 2016 6:53 AM
To: Mark Sale
Cc: [email protected]
Subject: Re: [NMusers] $PRIOR with normal for OMEGA?
Mark,
Without getting too technical, recall that the inverse wishart is a
distribution on matrices, and is naturally conjugate to the multivariate normal
distribution (i.e. on vectors of random variables.) Generally, this is chosen
because posterior computations are simplified and it is easy to sample from
this posterior distribution.
What you're suggesting is the Matrix Normal distribution. Since it is not
conjugate to the multivariate normal, posterior computations can cause
headaches. So while it is *possible* to use such a distribution as a prior, it
is cumbersome to work with in practice and requires thinking about some things
like correlation and scale in non straightforward ways.
--------------
Andy Gewitz, PhD
Bioengineering and Therapeutic Sciences
University of California, San Francisco
On Nov 10, 2016, at 7:57 PM, Mark Sale
<[email protected]<mailto:[email protected]>> wrote:
Is it possible to use a normal prior for OMEGA? The default is inverse Wishart,
but I'd be interested in using Normal (insuring that it is positive definite)
Any ideas?
thanks
Mark Sale M.D.
Vice President, Modeling and Simulation
Nuventra Pharma Sciences, Inc.
2525 Meridian Parkway, Suite 280
Durham, NC 27713
Phone (919)-973-0383
[email protected]<[email protected]>
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