[R] The gradient of a multivariate normal density with respecttoits parameters

[Ravi Varadhan]

Karl,

I have written a function to compute the gradient of a multivariate normal
density (derivatives at a given point, with respect to the parameters of the
density).  It is in the atttached file.  I would appreciate any feedback.

There are couple of interesting points: 

1.  Note is that there is a minor adjustment needed to the formulas given by
Dwyer (Table 2, Eqs. (11.7 and 11.8) to account for the symmetry in the
derivatives of the covariance parameters.  Without this adjustment the
derivatives of covariances are off by a factor of 2.

2.  I couldn't figure out how to avoid inverting the covariance matrix for
Eq. (11.7), using `solve(sigma)'.  I would appreciate knowing if there is a
trick for doing this.

Ravi. 


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Ravi Varadhan, Ph.D.

Assistant Professor, The Center on Aging and Health

Division of Geriatric Medicine and Gerontology 

Johns Hopkins University

Ph: (410) 502-2619

Fax: (410) 614-9625

Email: rvaradhan at jhmi.edu

Webpage:
http://www.jhsph.edu/agingandhealth/People/Faculty_personal_pages/Varadhan.h
tml

 

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-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On
Behalf Of Karl Ove Hufthammer
Sent: Wednesday, June 24, 2009 3:21 AM
To: r-help at stat.math.ethz.ch
Subject: Re: [R] The gradient of a multivariate normal density with
respecttoits parameters

Ravi Varadhan:

> You may want to look at the paper by Dwyer on "Some applications of 
> matrix derivatives in multivariate analysis" (JASA 1967), especially 
> the Table 2 on p. 617.

Thanks! That's a *very* useful paper. Note there also is a small corrigenda
available:

Corrigenda: Some Applications of Matrix Derivatives in Multivariate Analysis
Paul S. Dwyer Journal of the American Statistical Association, Vol. 62, No.
320 (Dec., 1967), p. 1518 Stable URL: http://www.jstor.org/stable/2283811

--
Karl Ove Hufthammer

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