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Suppose that I have two variables, $X$ and $Y$ that I want to correlate, i.e. in the manner of a scatterplot of $(X_i,Y_i)$. But I also want to show the density of each variable. A scatterplot basically does this, but I wanted a more organic display in the fashion of a KDE.

How can I make a plot where $\mathrm{dens}(x,y) = K(X,x,Y,y)$? I imagine plotting $\mathrm{dens}(x,y)$ either as a third variable with a 3D design if the distributions are simple or as pixel color intensity/value.

A sample kernel in this example would be the product of the KDEs for each respective variable.

A motivating example would be to observe bivariate "islands" in heteroscedastic data.

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  • $\begingroup$ Something like this? en.wikipedia.org/wiki/File:MultivariateNormal.png $\endgroup$ – bdeonovic Oct 15 '14 at 3:18
  • $\begingroup$ @Benjamin Not really. Picture a scatterplot except with a properly sized 2D normal distribution superimposed on each point. (shading is fine) $\endgroup$ – Simon Kuang Oct 15 '14 at 3:28
  • $\begingroup$ ggplot2 can do this using stat_density2d: google.com/… $\endgroup$ – ziggystar Oct 15 '14 at 7:30
  • $\begingroup$ Perhaps you are looking for something like the image I posted in an answer at stats.stackexchange.com/a/114238, which superimposes the scatterplot over a KDE of the bivariate data with two more (discrete) variables symbolized by color and symbol type. The post includes R code to produce the figure. $\endgroup$ – whuber Oct 15 '14 at 18:52
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Package ggplot2 can do this using stat_density2d, see the documentation.

enter image description here

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  • $\begingroup$ Also see the overlaid contours on the scatterplot in the documentation link provided above! $\endgroup$ – Dianne Cook Oct 15 '14 at 16:10

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