[R] Computing multivariate normal probabilities. Was: Re: Problem with Numerical derivatives (numDeriv) and mvtnorm

[Torsten Hothorn]

On Sun, 22 Nov 2009, Ravi Varadhan wrote:

>
> Hi Torsten,
>

Hi Ravi,

> It would be useful to "warn" the users that the multivariate normal probability
> calculated by "pmvnorm" using the GenzBretz algorithm is "random", i.e. 
> the result can vary between repeated executions of the function.

only if a different seed is used.

> This 
> would prevent inappropriate use of pmvnorm such as computing derivatives 
> of it (see this email thread).
>

?pmvt has "Randomized quasi-Monte Carlo methods are used for the
computations." and appropriate references. In addition, the new book by 
Alan Genz and Frank Bretz covers all technical details in depth, so
the procedures are well documented.

Anyway, I'll add a statement to ?pmvnorm.

Best wishes,

Torsten