If you want exact ellipses corresponding to a specific bivariate normal,
consider the following:
Info <- array(c(2, 1,1,2), dim=c(2,2))
Q.form <-
function(x, y, mu=c(0, 1), Info.=Info){
z0 <- (c(x, y)-mu)
Q. <- (t(z0) %*% Info %*% z0)
}
###########
Info. = inverse of the covariance matrix.
Put this into a loop to generate the grid of points to plot with
contour or persp.
hope this helps. spencer graves
Pedram Sendi wrote:
Deal all
Further to my e-mail with respect to drawing confidence ellipses
around 5000 pairs of values, I was not successful with kde2d. I am not
sure whether this is the answer to my question (I realise that I did
not provide sufficient information).
Attached is a plot of the 5000 samples I have, which approximate a
bivariate normal distribution (with a positive correlation). I'd be
interested in fitting smooth ellipses that include 5%, 50% and 95% of
the 5000 samples. I would be very grateful if someone could tell me
how to do it in S-Plus (v 6.1 for win).
Thanks a lot!
Best,
Pedram
Pedram Sendi, MD, DSc
Institute for Clinical Epidemiology & Division of Infectious Diseases
Institut fur klinische Epidemiologie & Abteilung fur Infektiologie
Basel University Hospital
Kantonsspital Basel
Hebelstrasse 10, 3rd Floor
CH-4031 Basel
Switzerland
Phone: +41 61 265 31 02
Fax: +41 61 265 31 09
On Tue, 16 Sep 2003 09:44:12 +0100 (GMT Dayligh, Prof Brian D Ripley
wrote:
>On Tue, 16 Sep 2003, Pedram Sendi wrote:
>
>>I have approximated a bivariate distribution f(a,b) using
>>simulation, i.e.
>>I have 5000 values of pairs of a,b. I would now like to plot a
>>smooth 95%
>>confidence ellipse, 50% confidence ellipse and 5% confidence
>>ellipse. The
>>contour plot feature does not seem to work. I would be very
>>grateful if
>>someone could tell me how to accomplish this in S-Plus 6.1 for
>>Windows.
>
>So you approximated a density by 5000 point values? That's not a
>very good
>approximation! What makes you think that there is a confidence
>ellipse (as
>distinct from any other shape of region)? And do you mean a
>confidence
>region, which needs a parametrized model?
>
>What I can help with is finding a contour plot of the underlying
>density.
>First find a 2d density estimate (using e.g. kde2d in MASS or the
>functions
>in KernSmooth), and compute the density values of your 5000 points,
>and
>sort them. Then the 5%, 50% and 95% quantiles of those density
>values can
>be used as contour levels for a plot of the density estimate
>(evaluated at
>a rectangular grid). That's the best interpretation I can find of
>your
>intentions. You will find relevant examples in MASS (the book).
>
>An alternative interpretation would be to assume a bivariate normal
>or t
>distribution (which have elliptical contours), fit that and then
>plot the
>appropriate density contours.
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