It’s true that models are maps. It’s also true, to recall a George Box quote, that “all models are false but some are useful”.
I agree that
The relevant thing for a model is how well it gets you to where you want to go
...and that, to my mind, supports the notion of the “probability of a model”, or, rather, the “probability of this particular model being sufficiently good to get you to where you want to go”.
I think it’s a fairly practical concept—if I’m modeling something and I am fitting several models which give me various trade-offs, it’s useful for me to think in terms of, say, the probability that a linear model will be sufficient for my purposes. If I define my purposes rigorously enough, the “model is sufficient” becomes a proposition.
But in a more general and more handwavy sense, I think it’s fine to assign to whole maps the probability of being correct. Take a literal example, say a nautical chart. Let’s say I have a chart of a coast unknown to me and as I explore it, I find that the chart is partially correct, but partially off. It depicts this peninsula, but fails to show that rock and the sandbar on the chart doesn’t exist in reality. After a while my belief in the accuracy of chart becomes partial so when I go around a point and the chart says there will be shoals, I expect to actually find these shoals with the probability of X%.
It’s true that models are maps. It’s also true, to recall a George Box quote, that “all models are false but some are useful”.
I agree that
...and that, to my mind, supports the notion of the “probability of a model”, or, rather, the “probability of this particular model being sufficiently good to get you to where you want to go”.
I think it’s a fairly practical concept—if I’m modeling something and I am fitting several models which give me various trade-offs, it’s useful for me to think in terms of, say, the probability that a linear model will be sufficient for my purposes. If I define my purposes rigorously enough, the “model is sufficient” becomes a proposition.
But in a more general and more handwavy sense, I think it’s fine to assign to whole maps the probability of being correct. Take a literal example, say a nautical chart. Let’s say I have a chart of a coast unknown to me and as I explore it, I find that the chart is partially correct, but partially off. It depicts this peninsula, but fails to show that rock and the sandbar on the chart doesn’t exist in reality. After a while my belief in the accuracy of chart becomes partial so when I go around a point and the chart says there will be shoals, I expect to actually find these shoals with the probability of X%.