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> Also assuming normal distribution, I think? 95% is 95% regardless of the distribution. > I would like to build some edge into my bets. If a reader takes bot

> Also assuming normal distribution, I think? 95% is 95% regardless of the distribution. > I would like to build some edge into my bets. If a reader takes both sides of your example, they would be come out exactly even. You can imagine yourself being equally unhappy to take either side of the bet, if that's easier than imagining yourself being happy to take either side. It is for me, which is probably something to bring up in therapy. I also think that framing things as bets brings in all the cultural baggage around gambling and so it isn't always helpful. I'm not sure what a better framing is though.

eru 3y ago
> 95% is 95% regardless of the distribution. Standard deviation away from the mean don't correspond to the same percentiles for all distributions, or do they? If you want to be (almost) independent of distribution, you need Chebyshev's inequality. But that one is far weaker. > Its practical usage is similar to the 68–95–99.7 rule, which applies only to normal distributions. Chebyshev's inequality is more general, stating that a minimum of just 75% of values must lie within two standard deviations of the mean and 88.89% within three standard deviations for a broad range of different probability distributions.[1][2] https://en.wikipedia.org/wiki/Chebyshev%27s_inequality https://en.wikipedia.org/wiki/Chebyshev%27s_inequality > I also think that framing things as bets brings in all the cultural baggage around gambling and so it isn't always helpful. I'm not sure what a better framing is though. Underwriting insurance without going bankrupt, perhaps?
- jrumbut 3y ago
  > Standard deviation away from the mean don't correspond to the same percentiles for all distributions, or do they? If they had said a two standard deviation interval then you would have needed to know the distribution, but they said 95% which gives you all the information you need to make the bet.
  - eru 3y ago
    I was replying to this addendum, which only really works for the normal distribution: > Edit for OP's explicit question: One standard-deviation errorbars are 68% confidence intervals. Two standard deviations are 95% confidence intervals. (assuming you're a frequentist, of course) You are right about the first part of the original comment.

eru 3y ago

> 95% is 95% regardless of the distribution. Standard deviation away from the mean don't correspond to the same percentiles for all distributions, or do they? If you want to be (almost) independent of distribution, you need Chebyshev's inequality. But that one is far weaker. > Its practical usage is similar to the 68–95–99.7 rule, which applies only to normal distributions. Chebyshev's inequality is more general, stating that a minimum of just 75% of values must lie within two standard deviations of the mean and 88.89% within three standard deviations for a broad range of different probability distributions.[1][2] https://en.wikipedia.org/wiki/Chebyshev%27s_inequality https://en.wikipedia.org/wiki/Chebyshev%27s_inequality > I also think that framing things as bets brings in all the cultural baggage around gambling and so it isn't always helpful. I'm not sure what a better framing is though. Underwriting insurance without going bankrupt, perhaps?

jrumbut 3y ago
> Standard deviation away from the mean don't correspond to the same percentiles for all distributions, or do they? If they had said a two standard deviation interval then you would have needed to know the distribution, but they said 95% which gives you all the information you need to make the bet.
- eru 3y ago
  I was replying to this addendum, which only really works for the normal distribution: > Edit for OP's explicit question: One standard-deviation errorbars are 68% confidence intervals. Two standard deviations are 95% confidence intervals. (assuming you're a frequentist, of course) You are right about the first part of the original comment.