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This. Sometimes I feel like such out-of-touch-with-reality 'logic' is why a lot a people don't trust science anymore.

soared 10y ago
This is actually flawed logic.
whack 10y ago
Just because something is non-intuitive doesn't mean it's "out-of-touch-with-reality". Imagine if you go to a bus stop in a completely foreign city/country, and the bus shows up within 1 minute. There are 2 possibilities. Either A) The bus usually takes a very long time to come (30+ minutes) and you just happened to get very lucky, or B) The bus runs at a very frequent interval, so your 1-minute-wait is somewhat normal Statistically, B is much more likely to be true than A. Which is pretty much what the author is alluding to.
- semi-extrinsic 10y ago
  > Statistically, B is much more likely to be true than A. Which is pretty much what the author is alluding to. This depends entirely on what you mean by "statistically". Having travelled in many cities around the world, I have encountered many bus lines with long intervals, and not that many bus lines with very short intervals, so I would rather say A is statistically more likely than B. Discarding all previous data and then doing statistics is a great way to be wrong often IMO.
- pliny 10y ago
  You are using priors to decide that B is more likely than A, that is, you are saying that the frequent bus hypothesis is likely because buses with frequent intervals are common. If the bus shows up within 1 second of your arrival then there can be no discussion of "frequent buses", you were definitely lucky, but only because the prior for buses with frequency of Order-of (1 second) is so low. The analogy here is time-to-life and we have 1 data point for that, not enough to establish credible priors for minimum\mean time-to-life under any circumstances.
  - whack 10y ago
    The point of the thought experiment is to avoid using any priors. If you have a single data-point of an event E, taking time T to occur, then there are 2 possibilities: A) Event E usually takes much much longer than T (>100T), and what you just witnessed is an anomaly, or B) Event E usually does take roughly time T to occur, and what you witnessed is within the range of what usually occurs. Both conclusions have an extremely high likelihood of being wrong, since the sample size is so small. But between the 2, conclusion B is more likely to be true than conclusion A.

This is actually flawed logic.

whack 10y ago

Just because something is non-intuitive doesn't mean it's "out-of-touch-with-reality". Imagine if you go to a bus stop in a completely foreign city/country, and the bus shows up within 1 minute. There are 2 possibilities. Either A) The bus usually takes a very long time to come (30+ minutes) and you just happened to get very lucky, or B) The bus runs at a very frequent interval, so your 1-minute-wait is somewhat normal Statistically, B is much more likely to be true than A. Which is pretty much what the author is alluding to.

semi-extrinsic 10y ago
> Statistically, B is much more likely to be true than A. Which is pretty much what the author is alluding to. This depends entirely on what you mean by "statistically". Having travelled in many cities around the world, I have encountered many bus lines with long intervals, and not that many bus lines with very short intervals, so I would rather say A is statistically more likely than B. Discarding all previous data and then doing statistics is a great way to be wrong often IMO.
pliny 10y ago
You are using priors to decide that B is more likely than A, that is, you are saying that the frequent bus hypothesis is likely because buses with frequent intervals are common. If the bus shows up within 1 second of your arrival then there can be no discussion of "frequent buses", you were definitely lucky, but only because the prior for buses with frequency of Order-of (1 second) is so low. The analogy here is time-to-life and we have 1 data point for that, not enough to establish credible priors for minimum\mean time-to-life under any circumstances.
- whack 10y ago
  The point of the thought experiment is to avoid using any priors. If you have a single data-point of an event E, taking time T to occur, then there are 2 possibilities: A) Event E usually takes much much longer than T (>100T), and what you just witnessed is an anomaly, or B) Event E usually does take roughly time T to occur, and what you witnessed is within the range of what usually occurs. Both conclusions have an extremely high likelihood of being wrong, since the sample size is so small. But between the 2, conclusion B is more likely to be true than conclusion A.