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

[SL]

Hi Torsten,

Thanks for you comment.

If you have some free time to spare, partial derivatives with respect
to bounds and correlation coefficients would be great for pmvnorm! In
complex problems, optim is not very good at estimating the hessian
numerically and first order derivatives help to build an OPG
estimator, which is not very good as compared to an analytical hessian
but still much better than the numerical hessian provided by optim i
have found the problems I study.

Best,
Stephane

2009/11/23 Torsten Hothorn <Torsten.Hothorn at stat.uni-muenchen.de>:
>
> 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
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>