Thank you very much for your thoughts! Exactly what you mention is, what I am thinking about during the last hours: What is the relation between the den$z distribution and the z distribution. That's why I asked for ecdf(distribution)(value)->percentile earlier this day (thank you again for your quick and insightful answer on that!). I used it to compare certain values in both distributions by their percentile.
I really think you are completely right: I urgently need some lessons in bivariate/multivariate normal distributions. (I am a neurologist and unfortunately did not learn too much about statistics in university :-() I'll take your statement as a starter: "Once you go into two dimensions, SD loses all meaning, and adding nonparametric density estimation into the mix doesn't help, so just stop thinking in those terms!" This makes me really think a lot! Is plotting the 0,68 confidence interval in 2D as equivalent to +-1 SD really nonsense!? By the way: all started very harmless. I was asked to draw an example of the well known target analogy for accuracy and precision based on "real" (=simulated) data. (see i.e. http://en.wikipedia.org/wiki/Accuracy_and_precision for a simple hand made 2d graphic). Well, I did by set.seed(138813) x<-rnorm(n); y<-rnorm(n) plot(x,y) I was asked whether it might be possible to add a histogram with superimposed normal curve to the drawing: no problem. "And where is the standard deviation", well abline(v=sd(... OK. Then I realized, that this is of course only true for one of the distributions (x) and only in one "slice" of the scatterplot of x and y. The real thing is is a 3d density map above the scatterplot. A very nice example of this is demo(bivar) in the rgl package (for a picture see i.e http://rgl.neoscientists.org/gallery.shtml right upper corner). Great! But how to correctly draw the standard deviation boundaries for the "shots on the target" (the scatterplot of x and y)... I'd be grateful for hints on what to read on that matter (book, website etc.) Greetings from Munich, Felix. Am 03.03.12 19:22, schrieb peter dalgaard: > > On Mar 3, 2012, at 17:01 , drflxms wrote: > >> # this is the critical block, which I still do not comprehend in detail >> z <- array() >> for (i in 1:n){ >> z.x <- max(which(den$x < x[i])) >> z.y <- max(which(den$y < y[i])) >> z[i] <- den$z[z.x, z.y] >> } > > As far as I can tell, the point is to get at density values corresponding to > the values of (x,y) that you actually have in your sample, as opposed to > den$z which is for an extended grid of all possible (x_i, y_j) combinations. > > It's unclear to me what happens if you look at quantiles for the entire > den$z. I kind of suspect that it is some sort of approximate numerical > integration, but maybe not of the right thing.... > > Re SD: Once you go into two dimensions, SD loses all meaning, and adding > nonparametric density estimation into the mix doesn't help, so just stop > thinking in those terms! > ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
