I also had lots of confusion around this topic. I then stumbled upon Jaynes' "Probability theory" and that cleared up at least some of it. He states that probabilities merely encode our beliefs about uncertain situations. For "repeated" events these tie together with the frequencies, but for singular events they are less intuitive. Took me quite a long time to accept that probabilities are not something "existing" in the real world, but rather something "subjective" that reflects one's state of knowledge.
In the farming example above, the assumption is that it's equally likely that crop yield is well above, well below, or around average. That's just the best the farmer could come up with based on previous yields, or weather records and some knowledge about plant growth. Accepting that that's the best she can do in quantifying her uncertainty, she can then use decision theory to decide what actions to take.
But there's no "true model" in any sense as the world isn't stochastic as assumed in frequentist theory. Jaynes does a really nice job of making probability about handling uncertainty about singular events, and then shows how it can be applied.
Would be interested in what you think about Jaynes' book and the mind projection fallacy.
I love Jaynes and maximum entropy, but it's only part of the puzzle. Maximum entropy is a powerful way to predict the outcomes of thermodynamic systems. I'm less convinced it is useful for predicting the outcome of football games or elections.
I think the only way to approach stochastic reasoning is to have a fractured and piecemeal application of probability and statistics. Use it when it's appropriate, use something else when it's not.
Totally. Use it when you actually have to reason about uncertainty and drop it when the uncertainty becomes negligible, or it's easier to come up with a heuristic solution.
Sorry! It's a complicated and dumb inside joke. There is an aphorism:
"It's hard to make predictions, especially about the future."
But people love to claim it's a "quote" by famous people. Some people say it was said by Neils Bohr, but many others attribute it to Yogi Berra, the wisecracking coach of the New York Yankees baseball team. I always like how even history is often more story telling than factual.
Jake Soloff told me a good story when we were talking along these lines in August. Here is my paraphrasing of what he told me then: There was a famous Statistician (his exact identity escaping me) who was approached by the US Army during the Cold War. The general asked him "can you compute the probability whether the Russians will attack XYZ". And the Statistician, who was a frequentist, told the general something along the lines of "Look, they will attack or they won't -- I'm not sure those probabilities mean anything, I'm afraid I can't help you". The general said "I understand" and walked out of his office. Apparently, the famous Statistician said that turning the general away without helping him was one of the saddest moments of his professional career.
I guess this is a long way to agree with what you're getting at: all models (wait, no -- all formalisms even) are wrong, but we still want to strive to help others *do something useful*.
I don't know, untethered probabilistic prognostication is not useful by default. Sometimes it's better to say "I don't know."
Also, with regards to utility: people, including generals, make all sorts of decisions without setting odds or building probabilistic models. How do they do it? Can this be formalized? Should it be formalized? I don't have answers, but we should ask these questions.
I also had lots of confusion around this topic. I then stumbled upon Jaynes' "Probability theory" and that cleared up at least some of it. He states that probabilities merely encode our beliefs about uncertain situations. For "repeated" events these tie together with the frequencies, but for singular events they are less intuitive. Took me quite a long time to accept that probabilities are not something "existing" in the real world, but rather something "subjective" that reflects one's state of knowledge.
In the farming example above, the assumption is that it's equally likely that crop yield is well above, well below, or around average. That's just the best the farmer could come up with based on previous yields, or weather records and some knowledge about plant growth. Accepting that that's the best she can do in quantifying her uncertainty, she can then use decision theory to decide what actions to take.
But there's no "true model" in any sense as the world isn't stochastic as assumed in frequentist theory. Jaynes does a really nice job of making probability about handling uncertainty about singular events, and then shows how it can be applied.
Would be interested in what you think about Jaynes' book and the mind projection fallacy.
I love Jaynes and maximum entropy, but it's only part of the puzzle. Maximum entropy is a powerful way to predict the outcomes of thermodynamic systems. I'm less convinced it is useful for predicting the outcome of football games or elections.
I think the only way to approach stochastic reasoning is to have a fractured and piecemeal application of probability and statistics. Use it when it's appropriate, use something else when it's not.
Some of my thoughts about this here:
https://argmin.substack.com/p/a-dappled-world-of-probability
and here:
https://argmin.substack.com/p/from-proportion-to-causation
and here:
https://argmin.substack.com/p/learning-with-intentional-randomness
Totally. Use it when you actually have to reason about uncertainty and drop it when the uncertainty becomes negligible, or it's easier to come up with a heuristic solution.
Did some research on Yogi Berra to understand the title -- is he used as a metaphor for confusion and paradoxical statements?
Sorry! It's a complicated and dumb inside joke. There is an aphorism:
"It's hard to make predictions, especially about the future."
But people love to claim it's a "quote" by famous people. Some people say it was said by Neils Bohr, but many others attribute it to Yogi Berra, the wisecracking coach of the New York Yankees baseball team. I always like how even history is often more story telling than factual.
Anyway... my titles are all ridiculous.
Love the confusion.
Jake Soloff told me a good story when we were talking along these lines in August. Here is my paraphrasing of what he told me then: There was a famous Statistician (his exact identity escaping me) who was approached by the US Army during the Cold War. The general asked him "can you compute the probability whether the Russians will attack XYZ". And the Statistician, who was a frequentist, told the general something along the lines of "Look, they will attack or they won't -- I'm not sure those probabilities mean anything, I'm afraid I can't help you". The general said "I understand" and walked out of his office. Apparently, the famous Statistician said that turning the general away without helping him was one of the saddest moments of his professional career.
I guess this is a long way to agree with what you're getting at: all models (wait, no -- all formalisms even) are wrong, but we still want to strive to help others *do something useful*.
I don't know, untethered probabilistic prognostication is not useful by default. Sometimes it's better to say "I don't know."
Also, with regards to utility: people, including generals, make all sorts of decisions without setting odds or building probabilistic models. How do they do it? Can this be formalized? Should it be formalized? I don't have answers, but we should ask these questions.