Re: [R] Computing multivariate normal probabilities. Was: Re: Problem with Numerical derivatives (numDeriv) and mvtnorm
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@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.
Re: [R] Computing multivariate normal probabilities. Was: Re: Problem with Numerical derivatives (numDeriv) and mvtnorm
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.hoth...@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@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. __ R-help@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.
[R] Computing multivariate normal probabilities. Was: Re: Problem with Numerical derivatives (numDeriv) and mvtnorm
Hi Torsten,
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. This would
prevent inappropriate use of pmvnorm such as computing derivatives of it (see
this email thread).
It seems that the other algorithm Miwa is deterministic, but not sure how
reliable it is (I had some trouble with it).
It would also be useful in the help page to provide a link to two other
functions for evaluating multivariate normal probabilities:
mnormt::sadmvn
mprobit::mvnapp
In particular, the `mvnapp' function of Harry Joe in mprobit package seems to
be very interesting as it provides very accurate results using asymptotic
expansions.
Best,
Ravi.
Ravi Varadhan, Ph.D.
Assistant Professor,
Division of Geriatric Medicine and Gerontology
School of Medicine
Johns Hopkins University
Ph. (410) 502-2619
email: rvarad...@jhmi.edu
- Original Message -
From: Ravi Varadhan rvarad...@jhmi.edu
Date: Saturday, November 21, 2009 8:15 pm
Subject: Re: [R] Problem with Numerical derivatives (numDeriv) and mvtnorm
To: SL sl...@yahoo.fr
Cc: r-help@r-project.org
Go back to your calculus text and review the definition of derivative:
f'(x) = lim h - 0 [f(x+h) - f(x)] / h
when f(x) and f(x + h) are random variables, the above limit does not
exist. In fact, f'(x) is also a random variable.
Now, if you want the derivative you have to use a multivariate
integration algorithm that yields a deterministic value. The function
`sadmvn' in the package mnormt can do this:
require(mnormt)
PP2 - function(p){
thetac - p
thetae - 0.323340333
thetab - -0.280970036
thetao - 0.770768082
ssigma - diag(4)
ssigma[1,2] - 0.229502120
ssigma[1,3] - 0.677949335
ssigma[1,4] - 0.552907745
ssigma[2,3] - 0.784263100
ssigma[2,4] - 0.374065025
ssigma[3,4] - 0.799238700
ssigma[2,1] - ssigma[1,2]
ssigma[3,1] - ssigma[1,3]
ssigma[4,1] - ssigma[1,4]
ssigma[3,2] - ssigma[2,3]
ssigma[4,2] - ssigma[2,4]
ssigma[4,3] - ssigma[3,4]
pp - sadmvn(lower=rep(-Inf, 4),
upper=c(thetac,thetae,thetab,thetao), mean=rep(0,4), varcov=ssigma,
maxpt=10)
return(pp)
}
xx - -0.6675762
P2(xx)
require(numDeriv)
grad(x=xx, func=PP2)
I hope this helps,
Ravi.
Ravi Varadhan, Ph.D.
Assistant Professor,
Division of Geriatric Medicine and Gerontology
School of Medicine
Johns Hopkins University
Ph. (410) 502-2619
email: rvarad...@jhmi.edu
- Original Message -
From: SL sl...@yahoo.fr
Date: Saturday, November 21, 2009 2:42 pm
Subject: Re: [R] Problem with Numerical derivatives (numDeriv) and mvtnorm
To: r-help@r-project.org
Thanks for you comment.
There is certainly some Monte Carlo sampling involved in mvtnorm but
why derivatives could not be computed? In theory, the derivatives
exist (eg. bivariate probit). Moreover, when used with optim, there
are some numerical derivatives computed... does it mean that mvtnorm
cannot be used in an optimisation problem? I think it hard to believe.
One possibility would be to use the analytical derivatives and then
a
do-it-yourself integration but i was looking for something a bit more
comprehensive. The mvtnorm package uses a specific way to compute
pmvnorm and I'm far to do a good enough job so that derivatives can
compare with what mvtnorm can do.
Stef
__
R-help@r-project.org mailing list
PLEASE do read the posting guide
and provide commented, minimal, self-contained, reproducible code.
__
R-help@r-project.org mailing list
PLEASE do read the posting guide
and provide commented, minimal, self-contained, reproducible code.
__
R-help@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.
Re: [R] Computing multivariate normal probabilities. Was: Re: Problem with Numerical derivatives (numDeriv) and mvtnorm
I'm now making some trials with sadmvn which provides results similar
to pmvnorm for optimization but I know compute my OPG estimator of the
covariance matrix with sadmvn (by the way Ravi, when I was refering to
exist in theory I was refering to the theory not to the computation
- would an appropriate random computation of partial derivative
work?).
Interestingly, mprobit also provides derivatives, exactly what I need.
Unfortunatly it fails to install on mac os X! (I don't want to install
windows in my system and my linux server is off for the moment).
Stephane
2009/11/22 Ravi Varadhan rvarad...@jhmi.edu:
Hi Torsten,
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. This would prevent inappropriate use of pmvnorm such as computing
derivatives of it (see this email thread).
It seems that the other algorithm Miwa is deterministic, but not sure how
reliable it is (I had some trouble with it).
It would also be useful in the help page to provide a link to two other
functions for evaluating multivariate normal probabilities:
mnormt::sadmvn
mprobit::mvnapp
In particular, the `mvnapp' function of Harry Joe in mprobit package seems
to be very interesting as it provides very accurate results using asymptotic
expansions.
Best,
Ravi.
Ravi Varadhan, Ph.D.
Assistant Professor,
Division of Geriatric Medicine and Gerontology
School of Medicine
Johns Hopkins University
Ph. (410) 502-2619
email: rvarad...@jhmi.edu
- Original Message -
From: Ravi Varadhan rvarad...@jhmi.edu
Date: Saturday, November 21, 2009 8:15 pm
Subject: Re: [R] Problem with Numerical derivatives (numDeriv) and mvtnorm
To: SL sl...@yahoo.fr
Cc: r-help@r-project.org
Go back to your calculus text and review the definition of derivative:
f'(x) = lim h - 0 [f(x+h) - f(x)] / h
when f(x) and f(x + h) are random variables, the above limit does not
exist. In fact, f'(x) is also a random variable.
Now, if you want the derivative you have to use a multivariate
integration algorithm that yields a deterministic value. The function
`sadmvn' in the package mnormt can do this:
require(mnormt)
PP2 - function(p){
thetac - p
thetae - 0.323340333
thetab - -0.280970036
thetao - 0.770768082
ssigma - diag(4)
ssigma[1,2] - 0.229502120
ssigma[1,3] - 0.677949335
ssigma[1,4] - 0.552907745
ssigma[2,3] - 0.784263100
ssigma[2,4] - 0.374065025
ssigma[3,4] - 0.799238700
ssigma[2,1] - ssigma[1,2]
ssigma[3,1] - ssigma[1,3]
ssigma[4,1] - ssigma[1,4]
ssigma[3,2] - ssigma[2,3]
ssigma[4,2] - ssigma[2,4]
ssigma[4,3] - ssigma[3,4]
pp - sadmvn(lower=rep(-Inf, 4),
upper=c(thetac,thetae,thetab,thetao), mean=rep(0,4), varcov=ssigma,
maxpt=10)
return(pp)
}
xx - -0.6675762
P2(xx)
require(numDeriv)
grad(x=xx, func=PP2)
I hope this helps,
Ravi.
Ravi Varadhan, Ph.D.
Assistant Professor,
Division of Geriatric Medicine and Gerontology
School of Medicine
Johns Hopkins University
Ph. (410) 502-2619
email: rvarad...@jhmi.edu
- Original Message -
From: SL sl...@yahoo.fr
Date: Saturday, November 21, 2009 2:42 pm
Subject: Re: [R] Problem with Numerical derivatives (numDeriv) and mvtnorm
To: r-help@r-project.org
Thanks for you comment.
There is certainly some Monte Carlo sampling involved in mvtnorm but
why derivatives could not be computed? In theory, the derivatives
exist (eg. bivariate probit). Moreover, when used with optim, there
are some numerical derivatives computed... does it mean that mvtnorm
cannot be used in an optimisation problem? I think it hard to believe.
One possibility would be to use the analytical derivatives and then
a
do-it-yourself integration but i was looking for something a bit more
comprehensive. The mvtnorm package uses a specific way to compute
pmvnorm and I'm far to do a good enough job so that derivatives can
compare with what mvtnorm can do.
Stef
__
R-help@r-project.org mailing list
PLEASE do read the posting guide
and provide commented, minimal, self-contained, reproducible code.
__
R-help@r-project.org mailing list
PLEASE do read the posting guide
and provide commented, minimal, self-contained, reproducible code.
__
R-help@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.
__
