Possible, yes (see fortune('Yoda')), but doing it can be a bit difficult.
Here is one approximation using an independent normal kernel in 2 dimensions:
kde.contour - function(x,y=NULL, conf=0.95, xdiv=100, ydiv=100, kernel.sd ) {
xy - xy.coords(x,y)
xr - range(xy$x)
yr - range(xy$y)
xr - xr + c(-1,1)*0.1*diff(xr)
yr - yr + c(-1,1)*0.1*diff(yr)
if(missing(kernel.sd)) {
kernel.sd - c( diff(xr)/6, diff(yr)/6 )
} else if (length(kernel.sd)==1) {
kernel.sd - rep(kernel.sd, 2)
}
xs - seq(xr[1], xr[2], length.out=xdiv)
ys - seq(yr[1], yr[2], length.out=ydiv)
mydf - expand.grid( xx=xs, yy=ys )
tmpfun - function(xx,yy) {
sum( dnorm(xx, xy$x, kernel.sd[1]) * dnorm(yy, xy$y,
kernel.sd[2]) )
}
z - mapply(tmpfun, xx=mydf$xx, yy=mydf$yy)
sz - sort(z, decreasing=TRUE)
cz - cumsum(sz)
cz - cz/cz[length(cz)]
cutoff - sz[ which( cz conf )[1] ]
plot(xy, xlab='x', ylab='y', xlim=xr, ylim=yr)
#contour( xs, ys, matrix(z, nrow=xdiv), add=TRUE, col='blue')
contour( xs, ys, matrix(z, nrow=xdiv), add=TRUE, col='red',
levels=cutoff, labels='')
invisible(NULL)
}
# test
kde.contour( rnorm(100), rnorm(100) )
# correlated data
my.xy - MASS::mvrnorm(100, c(3,10), matrix( c(1,.8,.8,1), 2) )
kde.contour( my.xy, kernel.sd=.5 )
# compare to theoritical
lines(ellipse::ellipse( 0.8, scale=c(1,1), centre=c(3,10)), col='green')
# bimodal
new.xy - rbind( MASS::mvrnorm(65, c(3,10), matrix( c(1,.6,.6,1),2) ),
MASS::mvrnorm(35, c(6, 7), matrix( c(1,.6,.6,1), 2) ) )
kde.contour( new.xy, kernel.sd=.75 )
For more than 2 dimensions it becomes more difficult (both to visualize and to
find the region, contour only works in 2 dimensions). You can also see that
the approximations are not great compared to the true theory, but possibly a
better kernel would improve that.
Hope this helps,
--
Gregory (Greg) L. Snow Ph.D.
Statistical Data Center
Intermountain Healthcare
[EMAIL PROTECTED]
801.408.8111
-Original Message-
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]
project.org] On Behalf Of Jeroen Ooms
Sent: Monday, December 08, 2008 5:54 AM
To: r-help@r-project.org
Subject: [R] Multivariate kernel density estimation
I would like to estimate a 95% highest density area for a multivariate
parameter space (In the context of anova). Unfortunately I have only
experience with univariate kernel density estimation, which is
remarkebly
easier :)
Using Gibbs, i have sampled from a posterior distirbution of an Anova
model
with k means (mu) and 1 common residual variance (s2). The means are
independent of eachother, but conditional on the residual variance. So
now I
have a data frame of say 10.000 iterations, and k+1 parameters.
I am especially interested in the posterior distribution of the mu
parameters, because I want to test the support for an inequalty
constrained
model (e.g. mu1 mu2 mu3). I wish to derive the multivariate 95%
highest
density parameter space for the mu parameters. For example, if I had a
posterior distirbution with 2 means, this should somehow result in the
circle or elipse that contains the 95% highest density area.
Is something like this possible in R? All tips are welcome.
--
View this message in context: http://www.nabble.com/Multivariate-
kernel-density-estimation-tp20894766p20894766.html
Sent from the R help mailing list archive at Nabble.com.
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