How to determine that validation and test set are statistically similar?

Hi everyone,

I have a dataset that I’ve had split in: training, validation, and test set. Anyway, as Andrew NG suggests, to avoid distribution shift from the training side to the test side, it’s preferable what I ask in the main topic.
In order to do that someone could say to use a frequentist statistical test (like t-test, chi-squared, and so on). Anyway, i would prefer to use a bayesian test (like this one in the PYMC3 tutorial), I would like to test what is called “histogram intersection” a sort of distance mainly used in computer vision tasks.

Do you have any suggestions on how to deal with this task?