Statistical plots have a lot of variety. Here we illustrate a fairly simple classification problem.

The idea is that we are given a set of training data in 2 classes and with 2 observed (or feature) variables. We assume that the measurements are bivariate Gaussian (normal) distributions in each case, but that the parameters are different in each case. The plot shows simulated data, and 2 of the ellipses indicate the mean, variance and covariance estimated separately for the 2 classes. Based on this a third ellipse has been drawn that passes between the others. A Bayesian interpretation is most straightforward. Using as prior probabilities the relative frequencies of classes in the training set, measurements on this ellipse have equal posterior probability of being in each of the 2 classes. For all other measurements, one class has a higher probability than the other.