Isn't there a very wide middle ground between (1) assigning 100% of your mental probability to a single model, like a normal curve and (2) assigning your mental probability proportionately across every conceivable model ala Solomonoff?
I mean the whole approach here sounds more philosophical than practical. If you have any kind of constraint on your computing power, and you are trying to identify a model that most fully and simply explains a set of observed data, then it seems like the obvious way to use your computing power is to put about a quarter of your computing cycles on testing your preferred model, another quarter on testing mild variations on that model, another quarter on all different common distribution curves out of the back of your freshman statistics textbook, and the final quarter on brute-force fitting the data as best you can given that your priors about what kind of model to use for this data seem to be inaccurate.
I can't imagine any human being who is smart enough to run a statistical modeling exercise yet foolish enough to cycle between two peaks forever without ever questioning the assumption of a single peak, nor any human being foolish enough to test every imaginable hypothesis, even including hypotheses that are infinitely more complicated than the data they seek to explain. Why would we program computers (or design algorithms) to be stupider than we are? If you actually want to solve a problem, you try to get the computer to at least model your best cognitive features, if not improve on them. Am I missing something here?
Isn't there a very wide middle ground between (1) assigning 100% of your mental probability to a single model, like a normal curve and (2) assigning your mental probability proportionately across every conceivable model ala Solomonoff?
Yes, the question is what that middle ground looks like -- how you actually come up with new models. Gelman and Shalizi say it's a non-Bayesian process depending on human judgement. The behaviour that you rightly say is absurd, of the Bayesian Flying Dutchman, is indeed Shalizi's reductio ad absurdum of universal Bayesiani...
Here's the new thread for posting quotes, with the usual rules: