How do you define “works well” for a prior? I argue that for most things, the universal prior (everything is equally likely) works about as well as the lazy prior or Occam’s prior, because _all_ non-extreme priors are overwhelmed with evidence (including evidence from other agents) very rapidly. all three fail in the tails, but do just fine for the majority of uses.
Now if you talk about a measure of model simplicity and likelihood to apply to novel situations, rather than probability of prediciton, then it’s not clear that universal is usable, but it’s also not clear that lazy is better or worse than Occam.
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.
How do you define “works well” for a prior? I argue that for most things, the universal prior (everything is equally likely) works about as well as the lazy prior or Occam’s prior, because _all_ non-extreme priors are overwhelmed with evidence (including evidence from other agents) very rapidly. all three fail in the tails, but do just fine for the majority of uses.
Now if you talk about a measure of model simplicity and likelihood to apply to novel situations, rather than probability of prediciton, then it’s not clear that universal is usable, but it’s also not clear that lazy is better or worse than Occam.
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.