Hmm, the thing I find strange about this is that it doesn’t do something ‘more complicated’. To me, I would think to take a credal set of crisp causal laws, and then try to minimize the maximum regret (so a minimum of a maximum of a minimum of a maximum).
That is, Bayesians take multilevel models that give them a probability distribution over probability distributions. They then can compare how well they will do (in expectation) to how well someone who knew the distribution would do.
InfraBayesians should then take multilevel models that give them a hypothesis over hypotheses, that is, a credal set of credal sets. They then can compare how well they will do (in expectation, which for them means in minimax of expectation) to how well someone (where the someone is an infrabayesian) who knew the hypothesis would do.
Hmm, the thing I find strange about this is that it doesn’t do something ‘more complicated’. To me, I would think to take a credal set of crisp causal laws, and then try to minimize the maximum regret (so a minimum of a maximum of a minimum of a maximum).
That is, Bayesians take multilevel models that give them a probability distribution over probability distributions. They then can compare how well they will do (in expectation) to how well someone who knew the distribution would do.
InfraBayesians should then take multilevel models that give them a hypothesis over hypotheses, that is, a credal set of credal sets. They then can compare how well they will do (in expectation, which for them means in minimax of expectation) to how well someone (where the someone is an infrabayesian) who knew the hypothesis would do.
(I see after reading further that Vanessa mentioned this possibility)