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The article doesn't mention the problem that we often try to predict the outcome of a singular event when statistics can only tell us something about it when re

by lindig 10y ago

The article doesn't mention the problem that we often try to predict the outcome of a singular event when statistics can only tell us something about it when repeating it. The prediction could still be correct even when the actual event is not what was predicted.

tnecniv 10y ago
That, combined with the facts that humans have a poor intuition for probability and statistics and some results in the field seem inherently paradoxical (if you told a lay person that zero probability events happen all the time, they would look at you like you are crazy).
- Retric 10y ago
  That's just confusing numbers that approach zero with zero. Much like how guessing the lotto number has really low odds, but guessing that their will be a number has very good odds.
  - gizmo686 10y ago
    Not quite. Pick a random real number in the range [0,1]. Because there are an infinite amount of such numbers, the probability of picking any specific real number is precisely 0. However, you will still end up picking some number. EDIT: Fixed range
    - nitrogen 10y ago
      Assuming you meant [0,1], I don't think it's accurate to describe infinitesimals like lim->0 as being equal to zero. Adding an infinite number of infinitesimals gives a nonzero result, but adding an infinite number of zeros does not.
    - mrob 10y ago
      Picking a random real number in the range [0,1] is impossible. The expected length of its simplest description is infinite, and if you cant describe it you haven't actually picked it.
      - soVeryTired 10y ago
        ...a uniformly distributed real number in the range [0, 1] :) Otherwise I can just pick 0 with probability 0.5 and 1 with probability 0.5. If you can't be pedantic when discussing maths, when can you be pedantic?
    - deleted 10y ago
      [deleted]
    - Retric 10y ago
      No it is (1 / infinity) which is not zero. Much like how X/X is not a continuous function even though the limits at 0 are 1.
      - gizmo686 10y ago
        Standard probability theory does not have a notion of infinitesimals. There have been non-standard attempts at probability theory that do involve such a notion. See [0] (found on a brief search; I have only skimmed). EDIT: Admittedly, the existence of the non-standards analysis is a good indication that this is an artifact of the formalization of probability theory; not of the underlying reality that we are trying to model. Simpson's paradox is probably a better example of a "real" "paradox" of probability. [1] [0] https://lirias.kuleuven.be/bitstream/123456789/551380/1/BenciHorstenWenmackers-BJPS-InfinitesimalProbabilities.pdf https://lirias.kuleuven.be/bitstream/123456789/551380/1/Benc... [1] https://en.wikipedia.org/wiki/Simpson's_paradox https://en.wikipedia.org/wiki/Simpson's_paradox
        abecedarius 10y ago
        https://www.amazon.com/Radically-Elementary-Probability-Theory-AM-117/dp/0691084742 https://www.amazon.com/Radically-Elementary-Probability-Theo... is apparently another take on this problem.
        Retric 10y ago
        While I don't disagree with what your saying, I would point out if you want to use specific definitions they don't apply in the general case. Abstractly, there must be some difference between 0.2 and 2 as the first is a valid output and the second is not. Otherwise when you sum [0.2,0.3] vs [2,3] you get the same probability of 0. But, there is a trade off that can make things a little cleaner if you define the probability at 0.2 to be 0.
  - jknoepfler 10y ago
    It isn't, actually. There is a difference between discrete and continuous probability distributions. Lotto numbers are a classic example of a discrete, finite space, and the probability of winning the lottery can be expressed precisely as a non-zero number. The probability of any individual event in a continuous probability distribution is exactly zero. You're free to dispute whether the continuum as a mathematical construct has validity when applied to the world of actual stuff, but that's a different debate and certainly doesn't have an obvious answer.
    - noobermin 10y ago
      That's why you don't quote probabilities from continuous PD's as "the probability of X" but of X falling between a range. It's like you're saying the area under a point on the graph is zero...duh.
    - mrob 10y ago
      It's not a different debate, it's an essential requirement for zero probability events to actually happen. For zero probability events to happen the observable universe needs to contain infinite bits of information. The true upper bound is subject to debate but it's widely believed to be finite (eg. below the Bekenstein bound). If it is finite, then by the pigeonhole principle, no method of sampling a continuous distribution can choose between more points from that distribution than can be enumerated by that many bits. This means the probability of making any specific selection is non-zero, because almost all of the distribution cannot be selected.
- WalterBright 10y ago
  Even statisticians routinely fall for cognitive biases when interpreting statistics. This was documented in "Thinking Fast Thinking Slow".
omginternets 10y ago
There's also something to be said for the replication crisis in certain highly-politicized fields of sociology and psychology. People (rightly, IMHO) realize that political activists sometimes work under the guise of scientific researchers. It shouldn't come as a surprise that this kind of conduct erodes confidence in the field as a whole. Sadly, the baby has a nasty habit of being thrown out with the bath water...
- pjc50 10y ago
  The replication crisis is not helped by the grant process, which demands ever more citable results but does not care about replication.
  - zigzigzag 10y ago
    This is a key problem fuelling climate change skepticism. People look at the structure of academia and notice that the way to get money in such a system is by convincing committees of your peers that your research is more important than other people's research. And saying "my research could literally save the world from total destruction" is the trump card in such a game, thus people are highly incentivised to play it.
- kem 10y ago
  Not disagreeing with you, but the replication crisis is happening everywhere, especially in the biomedical sciences. In fact, analyses have suggested it may be worse in certain fields, like cognitive neuroscience (whether or not you consider that a branch of psychology or biology is maybe debatable).
  - omginternets 10y ago
    Indeed, but I mention sociology and (social) psychology in particular because of their clear potential for political slant.
  - zigzigzag 10y ago
    Is it happening everywhere? I haven't heard of a replication crisis in physics, maths or computer science. There do seem to be problems with replication in studies of people.
chimeracoder 10y ago
> The prediction could still be correct even when the actual event is not what was predicted. This is true (and conversely, a prediction can still be "wrong" even if the outcome matches the prediction, if the prediction expresses the wrong degree of confidence). However: > when statistics can only tell us something about it when repeating it This is only true if you take a pure frequentist approach to probability. The Bayesian interpretation of probability has no problem with defining probabilities over single-occurrence events. (And even frequentists have a way of dealing with this, although Bayesians would argue that in doing so they're essentially adopting a form of Bayesian probability).

by lindig 10y ago

tnecniv 10y ago

That, combined with the facts that humans have a poor intuition for probability and statistics and some results in the field seem inherently paradoxical (if you told a lay person that zero probability events happen all the time, they would look at you like you are crazy).

Retric 10y ago
That's just confusing numbers that approach zero with zero. Much like how guessing the lotto number has really low odds, but guessing that their will be a number has very good odds.
- gizmo686 10y ago
  Not quite. Pick a random real number in the range [0,1]. Because there are an infinite amount of such numbers, the probability of picking any specific real number is precisely 0. However, you will still end up picking some number. EDIT: Fixed range
  - nitrogen 10y ago
    Assuming you meant [0,1], I don't think it's accurate to describe infinitesimals like lim->0 as being equal to zero. Adding an infinite number of infinitesimals gives a nonzero result, but adding an infinite number of zeros does not.
  - mrob 10y ago
    Picking a random real number in the range [0,1] is impossible. The expected length of its simplest description is infinite, and if you cant describe it you haven't actually picked it.
    - soVeryTired 10y ago
      ...a uniformly distributed real number in the range [0, 1] :) Otherwise I can just pick 0 with probability 0.5 and 1 with probability 0.5. If you can't be pedantic when discussing maths, when can you be pedantic?
  - deleted 10y ago
    [deleted]
  - Retric 10y ago
    No it is (1 / infinity) which is not zero. Much like how X/X is not a continuous function even though the limits at 0 are 1.
    - gizmo686 10y ago
      Standard probability theory does not have a notion of infinitesimals. There have been non-standard attempts at probability theory that do involve such a notion. See [0] (found on a brief search; I have only skimmed). EDIT: Admittedly, the existence of the non-standards analysis is a good indication that this is an artifact of the formalization of probability theory; not of the underlying reality that we are trying to model. Simpson's paradox is probably a better example of a "real" "paradox" of probability. [1] [0] https://lirias.kuleuven.be/bitstream/123456789/551380/1/BenciHorstenWenmackers-BJPS-InfinitesimalProbabilities.pdf https://lirias.kuleuven.be/bitstream/123456789/551380/1/Benc... [1] https://en.wikipedia.org/wiki/Simpson's_paradox https://en.wikipedia.org/wiki/Simpson's_paradox
      - abecedarius 10y ago
        https://www.amazon.com/Radically-Elementary-Probability-Theory-AM-117/dp/0691084742 https://www.amazon.com/Radically-Elementary-Probability-Theo... is apparently another take on this problem.
      - Retric 10y ago
        While I don't disagree with what your saying, I would point out if you want to use specific definitions they don't apply in the general case. Abstractly, there must be some difference between 0.2 and 2 as the first is a valid output and the second is not. Otherwise when you sum [0.2,0.3] vs [2,3] you get the same probability of 0. But, there is a trade off that can make things a little cleaner if you define the probability at 0.2 to be 0.
- jknoepfler 10y ago
  It isn't, actually. There is a difference between discrete and continuous probability distributions. Lotto numbers are a classic example of a discrete, finite space, and the probability of winning the lottery can be expressed precisely as a non-zero number. The probability of any individual event in a continuous probability distribution is exactly zero. You're free to dispute whether the continuum as a mathematical construct has validity when applied to the world of actual stuff, but that's a different debate and certainly doesn't have an obvious answer.
  - noobermin 10y ago
    That's why you don't quote probabilities from continuous PD's as "the probability of X" but of X falling between a range. It's like you're saying the area under a point on the graph is zero...duh.
  - mrob 10y ago
    It's not a different debate, it's an essential requirement for zero probability events to actually happen. For zero probability events to happen the observable universe needs to contain infinite bits of information. The true upper bound is subject to debate but it's widely believed to be finite (eg. below the Bekenstein bound). If it is finite, then by the pigeonhole principle, no method of sampling a continuous distribution can choose between more points from that distribution than can be enumerated by that many bits. This means the probability of making any specific selection is non-zero, because almost all of the distribution cannot be selected.
WalterBright 10y ago
Even statisticians routinely fall for cognitive biases when interpreting statistics. This was documented in "Thinking Fast Thinking Slow".

omginternets 10y ago

There's also something to be said for the replication crisis in certain highly-politicized fields of sociology and psychology. People (rightly, IMHO) realize that political activists sometimes work under the guise of scientific researchers. It shouldn't come as a surprise that this kind of conduct erodes confidence in the field as a whole. Sadly, the baby has a nasty habit of being thrown out with the bath water...

pjc50 10y ago
The replication crisis is not helped by the grant process, which demands ever more citable results but does not care about replication.
- zigzigzag 10y ago
  This is a key problem fuelling climate change skepticism. People look at the structure of academia and notice that the way to get money in such a system is by convincing committees of your peers that your research is more important than other people's research. And saying "my research could literally save the world from total destruction" is the trump card in such a game, thus people are highly incentivised to play it.
kem 10y ago
Not disagreeing with you, but the replication crisis is happening everywhere, especially in the biomedical sciences. In fact, analyses have suggested it may be worse in certain fields, like cognitive neuroscience (whether or not you consider that a branch of psychology or biology is maybe debatable).
- omginternets 10y ago
  Indeed, but I mention sociology and (social) psychology in particular because of their clear potential for political slant.
- zigzigzag 10y ago
  Is it happening everywhere? I haven't heard of a replication crisis in physics, maths or computer science. There do seem to be problems with replication in studies of people.

chimeracoder 10y ago

> The prediction could still be correct even when the actual event is not what was predicted. This is true (and conversely, a prediction can still be "wrong" even if the outcome matches the prediction, if the prediction expresses the wrong degree of confidence). However: > when statistics can only tell us something about it when repeating it This is only true if you take a pure frequentist approach to probability. The Bayesian interpretation of probability has no problem with defining probabilities over single-occurrence events. (And even frequentists have a way of dealing with this, although Bayesians would argue that in doing so they're essentially adopting a form of Bayesian probability).