You can divide your domain of integration into smaller intervals and then
add up the individual contributions. This could improve the speed of
adaptive Gauss-Kronrod quadrature used in integrate().
Ravi.
---
Ravi
- qr.solve(X,y)
all.equal(ans1,ans2)
[1] TRUE
Ravi.
---
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
An even simpler solution is:
mat2 - 1 * (mat1 0.25)
Ravi.
---
Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging and Health
Division of Geriatric Medicine and Gerontology
Johns Hopkins University
Another possibility is to use data squashing methods. Relevant papers are:
(1) DuMouchel et al. (1999), (2) Madigan et al. (2002), and (3) Owen (1999).
Ravi.
Ravi Varadhan, Ph.D.
Assistant Professor,
Division of Geriatric
that there can
be no correct solution to an ill-posed problem. Furthermore, I haven't
come across a real application where the numerical estimate of a rank is
directly useful.
Best,
Ravi.
---
Ravi Varadhan, Ph.D
.
---
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: [EMAIL PROTECTED
Tobias,
Just a clarification/correction to my solution: it makes no difference
whether A and B are positive or negative. The minimum of S1+S2-S3-S4 is
always -2(A+B).
Ravi.
---
Ravi Varadhan, Ph.D.
Assistant
.
---
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: [EMAIL PROTECTED]
Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html
.
---
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: [EMAIL PROTECTED
you'd like to do?
Ravi.
---
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
Hi Robin,
A Monte-Carlo approach could be attempted, if one could generate samples that
are either uniformly distributed over the simplex. There is a small section in
Luc Devroye's book (Generation of Non-uniform random deviates) on random
uniform sampling from a simplex, if I remeber
] 0.8264463
Hope this is helpful,
Ravi.
---
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
, the
larger the over-estimation. This is a well-known phenomenon in the
competing risks literature. See, for example, Gooley et al. (Stats in Med
1999).
Ravi.
---
Ravi Varadhan, Ph.D.
Assistant Professor, The Center
(N*th)/tan(th/2)) + cos(N*th))
}
This function works well, as you had expected.
Ravi.
---
Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging and Health
Division of Geriatric Medicine and Gerontology
Whether you can use optim or not depends on the nature of the constraints on
S. If you have simple box constraints, you can use the L-BFGS-B method in
optim. If not, optim may not be directly applicable, unless you can somehow
transform your problem into an unconstrained minimization problem.
If the constraints on S are linear inequalities, then linear programming
methods would work. See function solveLP in package linprog or simplex in
boot or package lpSolve.
Ravi.
- Original Message -
From: domenico pestalozzi [EMAIL PROTECTED]
Date: Wednesday, July 4, 2007 11:26 am
inequality constraints, but AFAIK those are not available in R.
Best,
Ravi.
---
Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging and Health
Division of Geriatric Medicine and Gerontology
Johns
is an
interior point, check to see whether the gradient there is close to zero.
Note that if the solution is one of the vertices of the polyhedron, then the
gradient may not be zero.
Ravi.
---
Ravi Varadhan, Ph.D.
Assistant
: Paul Smith [EMAIL PROTECTED]
Date: Tuesday, July 3, 2007 7:32 pm
Subject: Re: [R] Fine tunning rgenoud
To: R-help r-help@stat.math.ethz.ch
On 7/4/07, Ravi Varadhan [EMAIL PROTECTED] wrote:
It should be easy enough to check that your solution is valid (i.e.
a local
minimum): first, check
.
---
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: [EMAIL PROTECTED]
Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html
The PCs that are associated with the smaller eigenvalues.
---
Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging and Health
Division of Geriatric Medicine and Gerontology
Johns Hopkins University
Ph
Yes, Spencer, your observation is correct, because the characeristic equation
det(A - \lambda*I) is a sixth degree polynomial: \lambda^6 - 5 = 0. So the
eigenvalues are the complex numbers (generally) that are located at equal
angles on the circle of radius 5^(1/6), at angles 2*pi*k/6, where k
, the
Freudenstein-Roth function, shows the usefulness of the multiple random
starts.
Hope this is useful,
Ravi.
---
Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging and Health
Division of Geriatric
Hi,
You can use the function hessian() in the package numDeriv. This will
yield a very accurate estimate of the observed Fisher information matrix.
library(numDeriv)
?hessian
Ravi.
---
Ravi Varadhan, Ph.D
to a local optimum takes place, you simply restart the procedure
with another initial value.
Ravi.
---
Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging and Health
Division of Geriatric Medicine
(t)?
Ravi.
---
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
this is useful.
Best,
Ravi.
---
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
sometimes yield local minima which are not the zeros of the original
system. However, this can be easily remedied by using different starting
values.
Ravi.
---
Ravi Varadhan, Ph.D.
Assistant Professor, The Center
one
interested?
Ravi.
---
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
Perfect, Chuck. I got a closed-form solution after some algebraic labor,
but your solution is simple and elegant.
Ravi.
---
Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging and Health
Division
-20 7.474560e-25
Ravi.
---
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
.
---
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: [EMAIL PROTECTED]
Webpage: http
this is helpful,
Ravi.
---
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
y: 54.9 function: 0.00778
Of these, you can ignore the first 3, which have zero density.
Ravi.
---
Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging and Health
Division of Geriatric Medicine
.
---
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: [EMAIL PROTECTED]
Webpage: http
. In short, if you are sure that the numerical solution is
accurate, then you need to go back to your system of equations and analyze
them carefully.
Ravi.
---
Ravi Varadhan, Ph.D.
Assistant Professor, The Center
is accurate, then you need to go back to your system of
equations and analyze them carefully.
Ravi.
---
Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging and Health
Division of Geriatric Medicine
have to think about whether the resulting system of equations are
valid, when there are no A people.
Ravi.
---
Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging and Health
Division of Geriatric Medicine
appreciated.
Best,
Ravi.
---
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
Your data is compositional data. The R package compositions might be
useful. You might also want to consult the book by J. Aitchison: statistical
analysis of compositional data.
Ravi.
---
Ravi Varadhan, Ph.D
Dear Martin and Vitto,
Please find attached the R function to compute the density of the ratio of 2
dependent normal variates.
Best,
Ravi.
---
Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging
.
---
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: [EMAIL PROTECTED]
Webpage
.
---
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: [EMAIL PROTECTED]
Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty
.
---
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: [EMAIL PROTECTED]
Webpage: http
.
---
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: [EMAIL PROTECTED]
Webpage: http://www.jhsph.edu/agingandhealth/People
unconstrained minimization techniques.
Another good book is that by Roger Fletcher (1987): Practical methods of
optimization.
Ravi.
---
Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging and Health
Division
. If they are not
significantly different but the corresponding parameter estimates differ
widely, then you may have identifiability issues.
Ravi.
---
Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging and Health
Division
.
---
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: [EMAIL PROTECTED]
Webpage: http://www.jhsph.edu/agingandhealth/People
provided by R is correct or not. In the
case that I reported, it is fairly simple to see that the solution
provided by R (without any warning!) is incorrect, but, in general,
that is not so simple and one may take a wrong solution as a correct
one.
Paul
On 5/8/07, Ravi Varadhan
.
---
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: [EMAIL PROTECTED]
Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty
point).
However, I do not why optim converges to the boundary maximum, when analytic
gradient is supplied (as shown by Sundar).
Ravi.
---
Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging and Health
Harold,
I totally echo your sentiments on the difficulty of creating an R package in
Windows. I really wish that this process could be made a bit less painful.
Ravi.
---
Ravi Varadhan, Ph.D.
Assistant
Check out the function mvrnorm in package MASS.
library(MASS)
?mvrnorm
Ravi.
---
Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging and Health
Division of Geriatric Medicine and Gerontology
Johns
.
---
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: [EMAIL PROTECTED
.
---
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: [EMAIL PROTECTED]
Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty
.
---
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: [EMAIL PROTECTED]
Webpage: http://www.jhsph.edu
No.
---
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: [EMAIL
(1,
women$M, women$S))
out
$par
[1] -3.0612277 -1.4567141 0.3659251
$value
[1] 13.32251
$counts
function gradient
357 101
$convergence
[1] 1
$message
NULL
Hope this helps,
Ravi.
---
Ravi Varadhan
20 20 20 20 20 20 20
Looking forward to comments.
Best,
Ravi.
- Original Message -
From: Martin Maechler [EMAIL PROTECTED]
Date: Saturday, April 7, 2007 10:57 am
Subject: Re: [R] Computing the rank of a matrix.
To: Ravi Varadhan [EMAIL PROTECTED]
Cc: [EMAIL PROTECTED], 'José Luis
Hi,
qr(A)$rank will work, but just be wary of the tolerance parameter (default
is 1.e-07), since the rank computation could be sensitive to the tolerance
chosen.
Ravi.
---
Ravi Varadhan, Ph.D.
Assistant
) and different optimization methods (e.g. conjugate gradient with
Polak-Ribiere steplength option, Nelder-Mead, etc.).
Ravi.
---
Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging and Health
Division
c(HR) will do it.
Ravi.
---
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
Legendre, Laguerre polynomials.
Ravi.
---
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
.
---
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: [EMAIL PROTECTED
generally have slower convergence than QN type
methods, unless you can precondition the problem.
Hope this is helpful,
Ravi.
---
Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging and Health
Division
.
---
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: [EMAIL PROTECTED]
Webpage: http
be made to become arbitrarily large by letting the variance gets close
to zero, and in the limit you will obtain Dirac's delta function.
Ravi.
---
Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging
Your function jjj is not vectorized.
Try this:
jjj - function(www) sapply(www, function(x)2*integrate(dnorm,0,x)$value)
plot(jjj, 0, 5)
It should work.
Ravi.
---
Ravi Varadhan, Ph.D.
Assistant Professor
))
K - 1.2
ylang - rlangevin(n=10, mu=mu, K=K)
apply(ylang,1,crossprod)
[1] 1 1 1 1 1 1 1 1 1 1
I hope that this helps.
Ravi.
---
Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging and Health
Division
ifail
0.1250612 0.00999505459071123 0
Ravi.
---
Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging and Health
Division of Geriatric Medicine and Gerontology
Johns Hopkins
they should
be. If you don't, then you could try selfStart, as the error message tells
you to do.
Ravi.
---
Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging and Health
Division of Geriatric Medicine
dealing exclusively with
numeric mode.
Best,
Ravi.
---
Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging and Health
Division of Geriatric Medicine and Gerontology
Johns Hopkins University
Ph: (410) 502
], n, n)
}
mat
}
###
system.time(top.mat - toeplitz(runif(220)))
[1] 0.00 0.01 0.02 NA NA
Hope this is fast enough!
Best,
Ravi.
---
Ravi Varadhan, Ph.D.
Assistant
.
---
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: [EMAIL PROTECTED]
Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html
- sum(outer(x,x,FUN=fast.pmax))
+ sum333 - sum(outer(x,y,FUN=fast.pmax))
+ })
[1] 0.78 0.08 0.86 NA NA
all.equal(sum1,sum11,sum111)
[1] TRUE
all.equal(sum3,sum33,sum333)
[1] TRUE
---
Ravi Varadhan, Ph.D
.
---
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: [EMAIL PROTECTED]
Webpage: http://www.jhsph.edu/agingandhealth/People
two applys doesn't make the code any faster, it just produces
a compact one-liner.
Best,
Ravi.
---
Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging and Health
Division of Geriatric Medicine
.
---
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: [EMAIL PROTECTED
Jeff,
Here is something which is a little faster:
sum1 - sum(outer(x, x, FUN=pmax))
sum3 - sum(outer(x, y, FUN=pmax))
Best,
Ravi.
---
Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging and Health
Hi,
I have two matrices A (m x 2) and B (n x 2), where m and n are large integers
(on the order of 10^4). I am looking for an efficient way to create another
matrix, W (m x n), which can be defined as follows:
for (i in 1:m){
for (j in 1:n) {
W[i,j] - g(A[i,], B[j,])
} }
I have tried the
into a
maximization problem.
If this doesn't work, you should provide more details (a reproducible code
with actual error message).
Ravi.
---
Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging and Health
.
---
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: [EMAIL PROTECTED]
Webpage: http
.
---
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: [EMAIL PROTECTED]
Webpage: http
complete flexibility?
If it is possible, are you or anyone else in the R community working on
this?
Thanks,
Ravi.
---
Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging and Health
Division of Geriatric
Thanks, Roger. These should be very useful tools.
Ravi.
---
Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging and Health
Division of Geriatric Medicine and Gerontology
Johns Hopkins University
Ph
.
---
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: [EMAIL PROTECTED]
Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty
))
}
times - seq(0,30,by=0.1)
y0 - c(0,0)
parms - c(k1=0.7, k2=0.5, k3=0.2, k4=0.8, T=10, delay=5)
Is there a way to incorporate delay in odesolve?
Any hints would be much appreciated.
Ravi.
---
Ravi
-Original Message-
From: [EMAIL PROTECTED]
[mailto:[EMAIL PROTECTED] On Behalf Of Ravi Varadhan
Sent: Wednesday, November 29, 2006 4:45 PM
To: r-help@stat.math.ethz.ch
Subject: [R] How to solve differential equations
Thanks, Woodrow. I also found a DDE solver called dde23 in Matlab written
by L.F. Shampine. I will see if I can use it in Scilab, since I don't have
Matlab.
Ravi.
---
Ravi Varadhan, Ph.D.
Assistant Professor
to perform this computation
efficiently without the for loops?
Thank you,
Ravi.
---
Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging and Health
Division of Geriatric Medicine and Gerontology
-Original Message-
From: Christos Hatzis [mailto:[EMAIL PROTECTED]
Sent: Tuesday, November 14, 2006 2:49 PM
To: 'Dimitris Rizopoulos'; 'Ravi Varadhan'
Cc: r-help@stat.math.ethz.ch
Subject: RE: [R] Matrix-vector
Metcalf and Reid - FORTRAN 90/95 Explained
Ravi.
---
Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging and Health
Division of Geriatric Medicine and Gerontology
Johns Hopkins University
Ph: (410
of
grid points.
Ravi.
---
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
For heaven's sake, please stop sending repeat emails and send your R code
that can reproduce the error.
Ravi.
---
Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging and Health
Division of Geriatric
Also check out the package glmpath which can incorporate both ridge (L2)
and lasso (L1) type penalties.
Ravi.
---
Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging and Health
Division of Geriatric
.
pdf
I would also appreciate tips to any related algorithms/methods that are
implemented in R.
Thanks,
Ravi.
---
Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging and Health
Division
.
---
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: [EMAIL PROTECTED]
Webpage: http://www.jhsph.edu/agingandhealth
.
---
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: [EMAIL PROTECTED]
Webpage: http
weighted least squares.
Any help is appreciated.
Best,
Ravi.
---
Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging and Health
Division of Geriatric Medicine and Gerontology
Johns Hopkins
), which is a high-level modeling system for mathematical
programming and optimization.
Ravi.
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Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging and Health
Division of Geriatric Medicine
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