[R] The gradient of a multivariate normal density with respect to its parameters

[Karl Ove Hufthammer]

Ravi Varadhan skreiv:
> I am not aware of any.  May I ask what your purpose is?  You don't really
> need this if you are going to use it in optimization, since most optimizers
> use a simple finite-difference approximation if you don't provide the
> gradient.  Using the numerical approximation from "numDeriv" will be quite
> time-consuming in an optimization routine, since numDeriv uses a high-order
> Richardosn extrapolation to compute an accurate approximation of the
> gradient.
>   

No, I don’t use it in an optimisation. The expression is part of a more 
complicated formula used for calculating some estimates in a special 
nonparametric model.

I won’t use the numerical approximation; the alternative would be to 
calculate the analytical expressions myself. It’s not too difficult, but 
tedious, and the expressions I end up with may not be the fastest or 
most numerically accurate, so if there was a package implementing them 
in a good way, it would be nice. :)

> Regardless of your purpose, there is a small bug in your function.  You
> should change   `dmvnorm(cbind(x,y),mu,sig)'  to
> `dmvnorm(cbind(xx,yy),mu,sig)'.

Yes, of course. I originally used x and y when creating the example, but 
then discovered that the jacobian() function already used x as an 
argument for something else, so I renamed them to xx and yy (though 
obviously not everywhere!). I really should have tested it in a 
completely clean environment before posting.

-- 
Karl Ove Hufthammer