When assigning a probability to an event, try describing the event in different ways, and make sure your assigned probability transforms according to the above rules!
This seems like useful advice, but I don’t feel like any of the examples really get at applying it in a nontrivial way. I mean, the chances that you are in Canada are certainly at least as high as the chances you are in Ontario, CA, but the framework of functoriality seems like overkill for this simple observation. Can you give a natural example of a more nontrivial way that reasoning might go wrong that can be corrected with category theory?
I added in a section about Benford’s law, a surprising functorial prior on first digits of numbers in randomly compiled data!
However, I have the impression that one critique of the paper at the time was that functorial seems to just encompass a bunch of known cases in statistics like equivariance and exchangability. It’s hard to cook up a natural example that isn’t covered in one of those cases.
This seems like useful advice, but I don’t feel like any of the examples really get at applying it in a nontrivial way. I mean, the chances that you are in Canada are certainly at least as high as the chances you are in Ontario, CA, but the framework of functoriality seems like overkill for this simple observation. Can you give a natural example of a more nontrivial way that reasoning might go wrong that can be corrected with category theory?
I added in a section about Benford’s law, a surprising functorial prior on first digits of numbers in randomly compiled data!
However, I have the impression that one critique of the paper at the time was that functorial seems to just encompass a bunch of known cases in statistics like equivariance and exchangability. It’s hard to cook up a natural example that isn’t covered in one of those cases.
Well, I suppose that’s true abstracting the general pattern of these cases is potentially useful anyway.