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This is not a problem with Bayes' Theorem. Any alternative method of updating beliefs will suffer from exactly the same problem of noisy inputs, and have the th

This is not a problem with Bayes' Theorem. Any alternative method of updating beliefs will suffer from exactly the same problem of noisy inputs, and have the the additional problem that it cannot maintain consistency with all the evidence (which only Bayes' rule is capable of doing.) Using Bayes' rule consistently will make you aware of how uncertain the inputs are, and that is a feature, not a bug.

dimino 11y ago
How will it make you aware of uncertainty? At some point you do have to guess (called "estimating" here), do you not, and that will have a compounding effect on the outcome. You incorrectly guess a probability somewhere only by a small amount, and it multiplies its way through to the result, and you're looking at a potentially huge difference in resulting probability, which could easily span the "will act" or "won't act" gap.
- Houshalter 11y ago
  I think it's worth keeping the principles of bayesian reasoning in mind. The idea that you should update hypotheses on evidence, and adding probability in one place takes it from everywhere else slightly, keeping track of prior probability, etc. Not that you should actually do mental calculations on made up probability estimates. I mean you can do that, and if your estimates are at all decent, the result might be better. But I don't think anyone actually recommends that.
  - dimino 11y ago
    Judging from the content of lesswrong, I actually think literal math is what many people do recommend, and that's what bothers me.
    - TeMPOraL 11y ago
      In some cases you might want to actually do that math, even if you have to guesstimate numbers, since it still will beat your intuition. http://slatestarcodex.com/2013/05/02/if-its-worth-doing-its-worth-doing-with-made-up-statistics/ http://slatestarcodex.com/2013/05/02/if-its-worth-doing-its-... But in general, no one has enough computing power in their heads to go and do explicit bayesian updates on everything all day long. You have to pick your battles, and use the right tools for the task at hand.
      - davidgerard 11y ago
        That post is like nobody there has ever heard the phrase "don't fall in love with your model". Quite a lot of LessWrong posts are of the theme "my model gives this counterintuitive result" - the trouble is they go on to "AND THIS IS VERY IMPORTANT AND SIGNIFICANT!!" rather than "hmm, maybe my model needs work."

dimino 11y ago

How will it make you aware of uncertainty? At some point you do have to guess (called "estimating" here), do you not, and that will have a compounding effect on the outcome. You incorrectly guess a probability somewhere only by a small amount, and it multiplies its way through to the result, and you're looking at a potentially huge difference in resulting probability, which could easily span the "will act" or "won't act" gap.

Houshalter 11y ago
I think it's worth keeping the principles of bayesian reasoning in mind. The idea that you should update hypotheses on evidence, and adding probability in one place takes it from everywhere else slightly, keeping track of prior probability, etc. Not that you should actually do mental calculations on made up probability estimates. I mean you can do that, and if your estimates are at all decent, the result might be better. But I don't think anyone actually recommends that.
- dimino 11y ago
  Judging from the content of lesswrong, I actually think literal math is what many people do recommend, and that's what bothers me.
  - TeMPOraL 11y ago
    In some cases you might want to actually do that math, even if you have to guesstimate numbers, since it still will beat your intuition. http://slatestarcodex.com/2013/05/02/if-its-worth-doing-its-worth-doing-with-made-up-statistics/ http://slatestarcodex.com/2013/05/02/if-its-worth-doing-its-... But in general, no one has enough computing power in their heads to go and do explicit bayesian updates on everything all day long. You have to pick your battles, and use the right tools for the task at hand.
    - davidgerard 11y ago
      That post is like nobody there has ever heard the phrase "don't fall in love with your model". Quite a lot of LessWrong posts are of the theme "my model gives this counterintuitive result" - the trouble is they go on to "AND THIS IS VERY IMPORTANT AND SIGNIFICANT!!" rather than "hmm, maybe my model needs work."