By “works well” I mean that we find whatever model we were looking for. Note that I didn’t say “eventually” (all priors work “eventually”, unless they assign too many 0 probabilities).
That seems susceptible to circularity. If we are looking for a simple model, we will get one. But what if we are looking for a true model? Is the simplest model necessarily true?
We aren’t looking for a simple model, we are looking for a model that generates accurate predictions. For instance, we could have two agents with two different priors independently working on the same problem (e.g. weather forecasting) for a fixed amount of time, and then see which of them found a more accurate model. Then, whoever wins gets to say that his prior is better. Nothing circular about it.
By “works well” I mean that we find whatever model we were looking for. Note that I didn’t say “eventually” (all priors work “eventually”, unless they assign too many 0 probabilities).
That seems susceptible to circularity. If we are looking for a simple model, we will get one. But what if we are looking for a true model? Is the simplest model necessarily true?
We aren’t looking for a simple model, we are looking for a model that generates accurate predictions. For instance, we could have two agents with two different priors independently working on the same problem (e.g. weather forecasting) for a fixed amount of time, and then see which of them found a more accurate model. Then, whoever wins gets to say that his prior is better. Nothing circular about it.