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Frequentism methods are strictly less general. For example Laplace used probability theory to estimate the mass of Saturn. But with a frequentist interpretation

by kccqzy 1y ago

Frequentism methods are strictly less general. For example Laplace used probability theory to estimate the mass of Saturn. But with a frequentist interpretation we have to imagine a large number of parallel universes where everything remains the same except for the mass of Saturn. That's overly prescriptive of what probability means. Whereas in Bayesian statistics what probability means is strictly more general. You can manipulate probabilities even without fully defining them (maximum entropy) subject to intuitive rules (sum rule, product rule, Bayes' theorem), and the results of such manipulation are still correct and useful.

deleted 1y ago
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perrygeo 1y ago
Drawing a sample of Saturns from an infinite set of Saturns! It's completely absurd, but that's what you get when you take a mathematical tool for coin flips and apply it to larger scientific questions. I wonder if the generality of the Bayesian approach is what's prevented its wide adoption? Having a prescribed algorithm ready to plug in data is mighty convenient! Frequentism lowered the barrier and let anyone run stats, but more isn't necessarily a good thing.
- IshKebab 1y ago
  I dunno about you guys but I have no problems imagining randomly sampling Saturn.
  - mitthrowaway2 1y ago
    What do you mean by "randomly sampling" here?
    - IshKebab 1y ago
      I mean, Saturn was formed by some process right? And it must be sensitive to some initial conditions that - although maybe not really random, we can treat as random. Now imagine going back in time and changing those conditions a bit so that Saturn ended up differently. Do that 1000 times, giving you 1000 different Saturns. Now pick one randomly.
      - chuckadams 1y ago
        We do that right now with computer simulations. Not exactly the hardest of evidence, but if the time machine were possible, someone in the future would have done it by now.
      - NeutralCrane 1y ago
        The point is that you can’t do that. That’s the entire conundrum with Frequentism. They object to stating anything about the probability of Saturn, because from an objectivist point of view, any statement is either true or it isn’t, and therefore all probabilistic statements about it must be 0% or 100%. Instead they resort to statements about the frequencies over the long term from repeated processes, like the one you have. There are two problems with this: 1. They aren’t answering the original question. The question is about the probability of a property of Saturn. Not about the process of repeatedly forming thousands of alternative Saturns. This seems like a subtle difference but that’s only because Frequentism has been the default for so long. It doesn’t attempt to answer the questions people are actually asking. 2. The assumptions it makes to answer that alternative question are just as flawed. We can’t go back in time and change the conditions surrounding Saturn’s creation. We can’t run 1000s of repeated trials of the creation of Saturn. For a group of people so ideologically opposed to a statement as simple as “the probability of this flipped coin being heads is 50%”, it seems absurd that they are fine with their entire framework being built around a premise that doesn’t exist and cannot exist.
      - rxtexit 1y ago
        In other words, creating a model that has little to do with reality then sampling from it to come up with a result that has little to do with reality. Yes, I think this is kind of standard practice in many fields. If someone questions this just quote "all models are wrong, but some are useful" as if the quote is actually saying "all models are wrong, but all models are useful".
StopDisinfo910 1y ago
Laplace is typical use of inference statistics to built an estimator. I don’t really understand your point about parallel universe here. It’s absolutely not necessary for any of the sampling to make sense. Every time you try to measure anything, you are indeed taking a sample of the set of measures you could have gotten given the tools you are using. I fear you operate under the illusion that frequentist statistics are somehow limited to hypothesis testing. It is absolutely not the case.
roenxi 1y ago
> But with a frequentist interpretation we have to imagine a large number of parallel universes where everything remains the same except for the mass of Saturn. That's overly prescriptive of what probability means. That isn't much of an argument to the mathematicians. Nobody ever came up with a compelling explanation for what -1 sheeps look like and yet negative numbers turned out to be extremely practical. If it is absurd and provably works then the math community can roll with that.
- kccqzy 1y ago
  It turns out -1 sheep is well defined: we use numbers to represent both absolute quantity and relative difference. A sheep died today, therefore the relative difference between today and yesterday is -1 sheep. Math people prefer to generalize. But with frequentism, it is not possible to generalize because "frequency" is baked into its very name. Indeed you can imagine Bayesian statistics as the generalization of frequentism.

by kccqzy 1y ago

deleted 1y ago

[deleted]

perrygeo 1y ago

Drawing a sample of Saturns from an infinite set of Saturns! It's completely absurd, but that's what you get when you take a mathematical tool for coin flips and apply it to larger scientific questions. I wonder if the generality of the Bayesian approach is what's prevented its wide adoption? Having a prescribed algorithm ready to plug in data is mighty convenient! Frequentism lowered the barrier and let anyone run stats, but more isn't necessarily a good thing.

IshKebab 1y ago
I dunno about you guys but I have no problems imagining randomly sampling Saturn.
- mitthrowaway2 1y ago
  What do you mean by "randomly sampling" here?
  - IshKebab 1y ago
    I mean, Saturn was formed by some process right? And it must be sensitive to some initial conditions that - although maybe not really random, we can treat as random. Now imagine going back in time and changing those conditions a bit so that Saturn ended up differently. Do that 1000 times, giving you 1000 different Saturns. Now pick one randomly.
    - chuckadams 1y ago
      We do that right now with computer simulations. Not exactly the hardest of evidence, but if the time machine were possible, someone in the future would have done it by now.
    - NeutralCrane 1y ago
      The point is that you can’t do that. That’s the entire conundrum with Frequentism. They object to stating anything about the probability of Saturn, because from an objectivist point of view, any statement is either true or it isn’t, and therefore all probabilistic statements about it must be 0% or 100%. Instead they resort to statements about the frequencies over the long term from repeated processes, like the one you have. There are two problems with this: 1. They aren’t answering the original question. The question is about the probability of a property of Saturn. Not about the process of repeatedly forming thousands of alternative Saturns. This seems like a subtle difference but that’s only because Frequentism has been the default for so long. It doesn’t attempt to answer the questions people are actually asking. 2. The assumptions it makes to answer that alternative question are just as flawed. We can’t go back in time and change the conditions surrounding Saturn’s creation. We can’t run 1000s of repeated trials of the creation of Saturn. For a group of people so ideologically opposed to a statement as simple as “the probability of this flipped coin being heads is 50%”, it seems absurd that they are fine with their entire framework being built around a premise that doesn’t exist and cannot exist.
    - rxtexit 1y ago
      In other words, creating a model that has little to do with reality then sampling from it to come up with a result that has little to do with reality. Yes, I think this is kind of standard practice in many fields. If someone questions this just quote "all models are wrong, but some are useful" as if the quote is actually saying "all models are wrong, but all models are useful".

StopDisinfo910 1y ago

Laplace is typical use of inference statistics to built an estimator. I don’t really understand your point about parallel universe here. It’s absolutely not necessary for any of the sampling to make sense. Every time you try to measure anything, you are indeed taking a sample of the set of measures you could have gotten given the tools you are using. I fear you operate under the illusion that frequentist statistics are somehow limited to hypothesis testing. It is absolutely not the case.

roenxi 1y ago

> But with a frequentist interpretation we have to imagine a large number of parallel universes where everything remains the same except for the mass of Saturn. That's overly prescriptive of what probability means. That isn't much of an argument to the mathematicians. Nobody ever came up with a compelling explanation for what -1 sheeps look like and yet negative numbers turned out to be extremely practical. If it is absurd and provably works then the math community can roll with that.

kccqzy 1y ago
It turns out -1 sheep is well defined: we use numbers to represent both absolute quantity and relative difference. A sheep died today, therefore the relative difference between today and yesterday is -1 sheep. Math people prefer to generalize. But with frequentism, it is not possible to generalize because "frequency" is baked into its very name. Indeed you can imagine Bayesian statistics as the generalization of frequentism.