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JQuinton comments on Rationality Quotes December 2014 - Less Wrong
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Wouldn't something good happening correctly result in a Bayseian update on the probability that you are a genius, and something bad a Bayseian update on the probability that someone is an idiot? (perhaps even you)
Yes, but if something good happens you have to update on the probability that someone besides you is a genius, and if something bad happens you have to update on the probability that you're the idiot. The problem is people only update the parts that make them look better.
Yes, but the issue is whether or not those are the dominant hypotheses that come to mind. It's better to see success and failure as results of plans and facts than innate ability or disability.
Not without a causal link, the absence of which is conspicuous.
Not necessarily. Causation might not be present, true, but causation is not necessary for correlation, and statistical correlation is what Bayes is all about. Correlation often implies causation, and even when it doesn't, it should still be respected as a real statistical phenomenon. All Jiro's update would require is that P(success|genius) > P(success|~genius), which I don't think is too hard to grant. It might not update enough to make the hypothesis the dominant hypothesis, true, but the update definitely occurs.
"Because" (in the original quote) is about causality. Your inequality implies nothing causal without a lot of assumptions. I don't understand what your setup is for increasing belief about a causal link based on an observed correlation (not saying it is impossible, but I think it would be helpful to be precise here).
Jiro's comment is correct but a non-sequitur because he was (correctly) pointing out there is a dependence between success and genius that you can exploit to update. But that is not what the original quote was talking about at all, it was talking about an incorrect, self-serving assignment of a causal link in a complicated situation.
Yes, naturally. I suppose I should have made myself a little clearer there; I was not making any reference to the original quote, but rather to Jiro's comment, which makes no mention of causation, only Bayesian updates.
Because P(causation|correlation) > P(causation|~correlation). That is, it's more likely that a causal link exists if you see a correlation than if you don't see a correlation.
As for your second paragraph, Jiro himself/herself has come to clarify, so I don't think it's necessary (for me) to continue that particular discussion.
Where are you getting this? What are the numerical values of those probabilities?
You can have presence or absence of a correlation between A and B, coexisting with presence or absence of a causal arrow between A and B. All four combinations occur in ordinary, everyday phenomena.
I cannot see how to define, let alone measure, probabilities P(causation|correlation) and P(causation|~correlation) over all possible phenomena.
I also don't know what distinction you intend in other comments in this thread between "correlation" and "real correlation". This is what I understand by "correlation", and there is nothing I would contrast with this and call "real correlation".
Do you think it is literally equally likely that causation exists if you observe a correlation, and if you don't? That observing the presence or absence of a correlation should not change your probability estimate of a causal link at all? If not, then you acknowledge that P(causation|correlation) != P(causation|~correlation). Then it's just a question of which probability is greater. I assert that, intuitively, the former seems likely to be greater.
By "real correlation" I mean a correlation that is not simply an artifact of your statistical analysis, but is actually "present in the data", so to speak. Let me know if you still find this unclear. (For some examples of "unreal" correlations, take a look here.)
I think I have no way of assigning numbers to the quantities P(causation|correlation) and P(causation|~correlation) assessed over all examples of pairs of variables. If you do, tell me what numbers you get.
I asked why and you have said "intuition", which means that you don't know why.
My belief is different, but I also know why I hold it. Leaping from correlation to causation is never justified without reasons other than the correlation itself, reasons specific to the particular quantities being studied. Examples such as the one you just linked to illustrate why. There is no end of correlations that exist without a causal arrow between the two quantities. Merely observing a correlation tells you nothing about whether such an arrow exists. For what it's worth, I believe that is in accordance with the views of statisticians generally. If you want to overturn basic knowledge in statistics, you will need a lot more than a pronouncement of your intuition.
A correlation (or any other measure of statistical dependence) is something computed from the data. There is no such thing as a correlation not "present in the data".
What I think you mean by a "real correlation" seems to be an actual causal link, but that reduces your claim that "real correlation" implies causation to a tautology. What observations would you undertake to determine whether a correlation is, in your terms, a "real" correlation?
My original question was whether you think the probabilities are equal. This reply does not appear to address that question. Even if you have no way of assigning numbers, that does not imply that the three possibilities (>, =, <) are equally likely. Let's say we somehow did find those probabilities. Would you be willing to say, right now, that they would turn out to be equal (with high probability)?
Okay, here's my reasoning (which I thought was intuitively obvious, hence the talk of "intuition", but illusion of transparency, I guess):
The presence of a correlation between two variables means (among other things) that those two variables are statistically dependent. There are many ways for variables to be dependent, one of which is causation. When you observe that a correlation is present, you are effectively eliminating the possibility that the variables are independent. With this possibility gone, the remaining possibilities must increase in probability mass, i.e. become more likely, if we still want the total to sum to 1. This includes the possibility of causation. Thus, the probability of some causal link existing is higher after we observe a correlation than before: P(causation|correlation) > P(causation|~correlation).
If you are using a flawed or unsuitable analysis method, it is very possible for you to (seemingly) get a correlation when in fact no such correlation exists. An example of such a flawed method may be found here, where a correlation is found between ratios of quantities despite those quantities being statistically independent, thus giving the false impression that a correlation is present when it is actually not.
As I suggested in my reply to Lumifer, redundancy helps.
How will you be able to distinguish between the two?
You also seem to be using the word "correlation" to mean "any kind of relationship or dependency" which is not what it normally means.
Redundancy helps. Use multiple analysis methods, show someone else your results, etc. If everything turns out the way it's supposed to, then that's strong evidence that the correlation is "real".
EDIT: It appears I've been ninja'd. Yes, I am not using the term "correlation" in the technical sense, but in the colloquial sense of "any dependency". Sorry if that's been making things unclear.
The quote about causality is a characterization of an opponent's view. I was suggesting that the quote's author may have mischaracterized his opponent's view by interpreting a Bayseian update as an assertion of causality.