Good question. I think @avehtari could help in clarifying this.
Nowadays, I personally feel comfortable, if I have a large N, and if \mathrm{elpd}_{\mathrm{diff}} / \mathrm{SE}_{\mathrm{diff}} \geq 4. It would be wonderful if Aki could add a references to his FAQ which one can cite in papers to solidify this claim. In short, Aki’s post here:
is what we have to rely on at the moment :)