As far as I understand, Bhattacharyya's measure(s) can be used to see similarity between two empirical distributions. Other ways to do so are nicely explained here: Similarity measure between multiple distributions
Now, I have 10 mutually exclusive (and exhaustive) cuts of the space and have dependent variable falling into it. I've separate test data. Now the test data falls into these 10 cuts and I believe I can use Bhattacharyya's measures to compute how similar the test distribution is compared to the train distribution in each cut.
My question is, can I combine (for e.g. simply add) the value of the measures obtained across cuts to call it a "representative" of "goodness" of the model? And based on this measure, say, can I choose the best model?