Hi Rick

Cool. You can certainly do what you say, and the IML implementation is nice. I don't have time to play with it right now, but will do so ASAP (I hope this weekend).

But, while this definitely shows how to find points that are odder than expected on a given metric (Mahalnobis distance, in this case; clearly you could do something similar for other metrics) if the data are MVN (and, clearly, you could use some other distribution), does this really get at "outlier"?

(Here i am just sort of thinking in public.... these thoughts are fully developed, as will be obvious)

If you have (say) 1000 data points on data with 1000 variables, with some pairs highly correlated and others hardly at all (roughly a problem that I had where I used to work) then you expect 25 or so to be above the cutoff (and, of course, you could pick a different cutoff). But, then, that is what you would *expect*. This is similar to a one-dimensional case - if you sample a LOT of people, then some will be odd; if you sample 100,000 people you might expect to find a 7 foot tall person).

Further (and this could be investigated - or it may be known to theory) how does Mahalnobis distance work when only 1 pair of variables is weird, but neither alone is weird, and the other variables are fine? For example, if you reported that 1 % of people in a general population in the USA were widowed, that wouldn't be weird. And if you said 10 % were under 12 years old, that also wouldn't be weird. But if 0.1 % were widowed *and* under 12, that would be weird! In fact, even in a data set with 100,000 people, you might not expect a single widow under 12 years old.

OK, I'll stop babbling here. :-)