Re: confidence ellipses

[Pedram Sendi <psendi@uhbs.ch>]

Thanks for these hints. The approximated bivariate distribution is actually bivariate normal so I wouldn't expect something else than an ellipse. I will check the MASS book!

 

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

E-Mail: psendi@uhbs.ch

www.bice.ch

 

 

 

 

 

 

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.