Timeline for Absence of evidence is not evidence of absence: What does Bayesian probability have to say about it?
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
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| Mar 18, 2021 at 12:22 | comment | added | BCLC | ...is your round bracket remark addressing the principle of charity thing? | |
| Mar 18, 2021 at 12:21 | comment | added | BCLC | oh lol i didn't read the OP too thoroughly. now that i've read a little more of OP. is there perhaps some principle of charity violation here? i think the original aphorism is in the context of like...testing for cancer or something. negative result doesn't mean you don't have it. of course if without principle of charity you could just say 'hey actually a negative result decreases probability of positive result'...or something. i could've sworn i learned in statistics class like if something happens then we expect probability of it happening is high...or idk. but wait a minute... | |
| Mar 18, 2021 at 12:17 | comment | added | fblundun | @JohnSmithKyon the point of my post is to argue that it is actually not a true statement (as long as "absence of evidence" is interpreted to mean "absence of evidence for presence" rather than "absence of evidence for presence and absence of evidence against presence"). | |
| Mar 18, 2021 at 12:12 | comment | added | BCLC | absence of evidence is not evidence of absence --> afaik this is a true statement so why do you start with a true statement in a proof by contradiction? or wait, is there another statement that is false that you assume true (hoping to reach a contradiction)? | |
| Mar 18, 2021 at 12:10 | comment | added | fblundun | @JohnSmithKyon I meant "suppose absence of evidence were not evidence of absence" - the intention was to structure the post as a reductio ad absurdum, though in retrospect it might have been more readable to start with the premise that absence decreases the probability of evidence of presence and reason from there. | |
| Mar 18, 2021 at 11:50 | comment | added | BCLC | wait perhaps did you mean 'Suppose absence of evidence were evidence of absence' instead of were not ? | |
| Mar 18, 2021 at 11:49 | comment | added | BCLC | why did you delete your comment here? stats.stackexchange.com/questions/514471/… | |
| Mar 8, 2021 at 11:30 | comment | added | Nat | For example, the fact that a time-traveler hasn't come back to tell us about $X$ is evidence against $X .$ But if the probability of us not seeing a time-traveler coming back to tell us about $X$ isn't significantly affected by the probability of $X ,$ then the absence-of-evidence isn't significantly evidence-of-absence. | |
| Mar 8, 2021 at 11:21 | comment | added | Nat | The derivation of the final equation is spot-on, but the conclusion seems to miss the point: the claim can be proximally true. I mean, the OP asks about under what conditions is the claim true, and the above answer shows it: the claim is (proximally) true when$$\operatorname{P}\left(\text{no evidence}\right)~ \approx ~\operatorname{P}\left(\text{no evidence} \middle| \text{absence}\right) .$$ | |
| Mar 8, 2021 at 10:20 | comment | added | fblundun | @user76284 if we add the assumption that the tea investigation yields an absence of evidence that Bob didn't murder Sally, then the absence of evidence of presence (i.e. evidence of absence) and absence of evidence of absence (i.e. evidence of presence) might exactly cancel out, leaving our prior unchanged. (I don't actually think this should happen in the tea example - we act like the tea investigation result and murder hypothesis are independent only because the world is too complex for us to spend resources deciding whether the former is evidence for or against the latter.) | |
| Mar 8, 2021 at 7:23 | comment | added | innisfree | @user76284, right, the neatest way of making this point is to start by assuming that a observation would increase the plausibility of a theory | |
| Mar 8, 2021 at 5:49 | comment | added | user76284 | You misunderstood the example. The point is that the investigation revealed nothing about the murder in its conclusions. For all we know, its outcome could be more likely under the opposite hypothesis. | |
| Mar 8, 2021 at 1:05 | comment | added | fblundun | @user76284 no, learning that the tea price investigation yielded no evidence that Bob murdered Sally should indeed slightly decrease your probability that Bob murdered Sally, because it makes it less likely that Bob murdered Sally as part of a scheme to rig tea prices. To put it another way: if the investigation somehow had yielded evidence that Bob murdered Sally, that should increase your probability that Bob murdered Sally. So by the law of total probability, the investigation failing to yield such evidence must have the opposite effect. | |
| Mar 8, 2021 at 0:39 | comment | added | user76284 | “which means absence doesn't decrease the probability of evidence” That’s precisely the point, and it’s not absurd. Whether absence of evidence is evidence of absence depends on whether we would have expected that evidence under presence. Suppose an investigation of tea prices in China yields an absence of evidence that Bob murdered Sally. That doesn’t mean that it’s evidence of absence. | |
| Mar 7, 2021 at 14:36 | history | answered | fblundun | CC BY-SA 4.0 |