The Bhattacharyya distance does not satisfy the triangle inequality, so technically it is not a distance metric. The Hellinger distance may be more appropriate depending on the situation.

Thanks for sharing this, Joe Corliss. In which situations would you typically go with Hellinger distance over Bhattacharyya distance? I have not had much of practical utility of satisfying the triangle inequality when I used Bhattacharyya distance. I am wondering if you have used Hellinger distance before, when would you prefer it over Bhattacharyya? Thanks :)

I think in the context of this post, either is fine because they are both monotonic transformations of the Bhattacharyya coefficient (BC). So either way, you'll get the distribution with the highest BC. I don't know of a specific example where Hellinger is better, I would just prefer it because it agrees with our intuitive idea of distance.

The Bhattacharyya distance does not satisfy the triangle inequality, so technically it is not a distance metric. The Hellinger distance may be more appropriate depending on the situation.

Thanks for sharing this, Joe Corliss. In which situations would you typically go with Hellinger distance over Bhattacharyya distance? I have not had much of practical utility of satisfying the triangle inequality when I used Bhattacharyya distance. I am wondering if you have used Hellinger distance before, when would you prefer it over Bhattacharyya? Thanks :)

I think in the context of this post, either is fine because they are both monotonic transformations of the Bhattacharyya coefficient (BC). So either way, you'll get the distribution with the highest BC. I don't know of a specific example where Hellinger is better, I would just prefer it because it agrees with our intuitive idea of distance.