Bayesian model averaging struggles in practice because it accounts for uncertainty about which model is correct but still operates under the assumption that only one of them is.

Wait, what? That sounds significant. What does more than one model being correct mean?

Speculation before I read the paper:

I guess that's like modelling a process as the superposition of sub-processes? That would give the model more degrees of freedom with which to fit the data. Would we expect that to do strictly better than the mutual exclusion assumption, or does it require more data to overcome the degrees of freedom?

• If a single theory is correct, the mutex assumption will update toward it faster by giving it a higher prior, and the probability-distribution-over-averages would get there slower, but still assigns a substantial prior to theories close to the true one.

• On the other hand, if a combination is a better model, either because the true process is a superposition, or we are modelling something outside of our model-space, then a combination will be better able to express it. So mutex assumption will be forced to put all weight on a bad nearby theory, effectively updating in the wrong direction, whereas the combination won't lose as much because it contains more accurate models. I wonder if averaging combination will beat mutex assumption at every step?

Also interesting to note that the mutex assumption is a subset of the model space of the combination assumption, so if you are unsure which is correct, you can just add more weight to the mutex models in the combination prior and use that.

Now I'll read the paper. Let's see how I did.

"Bayesian model averaging struggles in practice because it accounts for uncertainty about which model is correct but still operates under the assumption that only one of them is."

Perhaps they should say "the assumption that exactly one model is perfectly correct"?