alt Hacker NewsAn interesting statistical example if you haven’t seen it before is the Anscombe Quartet :
https://en.wikipedia.org/wiki/Anscombe%27s_quartet
Four sets of X,Y datapoints that have exactly (or very close) common statistical parameters (mean, variance, correlation, linear regression, R^2), but with vastly different spatial distributions and “behavior” when looked at visually.
I have mostly worked with computational physics with discontinuous polynomial approximations. Stuff like this would be easily detected in those methods as anatomy brcsuse of assumption pf smoothness.
Statistics on the other hand is more accepting of discontinuous data due to it's basis in measure spaces.
Hence In general, you should know what your data should look like before you aim to detect anamolies. But also, it might be a good practice with new automated research actors to always use both approximations (measure theory based and otherwise), to figure out what's going on.