The Shape of Data

I recently finished reading Nate Silver’s book The Signal and the Noise, which has gotten me thinking about how exactly one should interpret models/probability distributions, and the predictions they make. (If you’ve read this book or plan to read it, I also recommend reading Cathy O’Neil’s review of it.) Ultimately what a model does is to make a claim about the probability that a certain statement is or is not true. I always found this idea slightly troubling, since any fact is either true or false; to say that a true statement has a 70% probability of being true seems kind of meaningless, even if you don’t know that it’s true. When you’re making predictions about future events, where the statements aren’t yet true or false at all, this seems even more problematic. But it turns out that one can make philosophical sense of these sorts of statements by…

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