[R] Multivariate kernel density estimation

Jeroen Ooms j.c.l.ooms at uu.nl
Mon Dec 8 13:54:04 CET 2008

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.
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