the claim that any prediction can be interpreted in this minimal and consistent framework without exceptions whatsoever is a rather strong claim
The Bayes Rule by itself is not a framework. It’s just a particular statistical operation, useful no doubt, but hardly arising to the level of framework.
The claim that you can interpret any prediction as forecasting a particular probability distribution has nothing to do with Bayes. For example, let’s say that an analyst predicts the average growth in the GDP of China for the next five years to be 5%. If we dig and poke we can re-express this as a forecast of something like a normal distribution centered at 5% and with some width which corresponds to the expected error—so there is your forecast probability distribution. But is there a particular prior here? Any specific pieces of evidence on which the analyst updated the prior? Um, not really.
The Bayes Rule by itself is not a framework. It’s just a particular statistical operation, useful no doubt, but hardly arising to the level of framework.
The claim that you can interpret any prediction as forecasting a particular probability distribution has nothing to do with Bayes. For example, let’s say that an analyst predicts the average growth in the GDP of China for the next five years to be 5%. If we dig and poke we can re-express this as a forecast of something like a normal distribution centered at 5% and with some width which corresponds to the expected error—so there is your forecast probability distribution. But is there a particular prior here? Any specific pieces of evidence on which the analyst updated the prior? Um, not really.