How to plot a contour line showing where 95% of values fall within, in R and in ggplot2

Question

Say we have:

x <- rnorm(1000)
y <- rnorm(1000)

How do I use ggplot2 to produce a plot containing the two following geoms:

<

Answer 1

I had an example where the MASS::kde2d() bandwidth specifications were not flexible enough, so I ended up using the ks package and the ks::kde() function and, as an example, the ks::Hscv() function to estimate flexible bandwidths that captured the smoothness better. This computation can be a bit slow, but it has much better performance in some situations. Here is a version of the above code for that example:

set.seed(1001)
d <- data.frame(x=rnorm(1000),y=rnorm(1000))
getLevel <- function(x,y,prob=0.95) {
    kk <- MASS::kde2d(x,y)
    dx <- diff(kk$x[1:2])
    dy <- diff(kk$y[1:2])
    sz <- sort(kk$z)
    c1 <- cumsum(sz) * dx * dy
    approx(c1, sz, xout = 1 - prob)$y
}
L95 <- getLevel(d$x,d$y)
library(ggplot2); theme_set(theme_bw())
ggplot(d,aes(x,y)) +
    stat_density2d(geom="tile", aes(fill = ..density..),
                   contour = FALSE)+
    stat_density2d(colour="red",breaks=L95)

## using ks::kde
hscv1 <- Hscv(d)
fhat <- ks::kde(d, H=hscv1, compute.cont=TRUE)

dimnames(fhat[['estimate']]) <- list(fhat[["eval.points"]][[1]], 
                                     fhat[["eval.points"]][[2]])
library(reshape2)
aa <- melt(fhat[['estimate']])

ggplot(aa, aes(x=Var1, y=Var2)) +
    geom_tile(aes(fill=value)) +
    geom_contour(aes(z=value), breaks=fhat[["cont"]]["50%"], color="red") +
    geom_contour(aes(z=value), breaks=fhat[["cont"]]["5%"], color="purple") 

For this particular example, the differences are minimal, but in an example where the bandwidth specification requires more flexibility, this modification may be important. Note that the 95% contour is specified using the breaks=fhat[["cont"]]["5%"], which I found a little bit counter-intuitive, because it is called here the "5% contour".