Re: [NMusers] $PRIOR with normal for OMEGA?

From: Gewitz, Andrew <Andrew.Gewitz_at_ucsf.edu>
Date: Fri, 11 Nov 2016 05:53:17 +0000

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 <msale_at_nuventra.com<mailto:msale_at_nuventra.com>> 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
msale_at_nuventra.com<msale_at_kinetigen.com>
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Received on Fri Nov 11 2016 - 00:53:17 EST

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