Sure, people should give it a go (especially if the value of their time is low enough that spending some of it on trying to use Firefox is not problematic even if there is a substantial chance of encountering serious problems). It’s just that they should be keenly aware that of what they’re doing when they give Firefox a go, and they should have Chrome (or similar) ready to go, so that they can switch at a moment’s notice if their Firefox experience goes poorly.
This seems totally non-responsive to the question, though (which did not mention evolution at all).
I must strongly disagree with the “use Firefox” recommendation.
Some links:
“Claude is totally broken in Firefox”
“Some examples of Firefox-specific fixes currently in use in my websites:”
Sticking it to the man is a noble ideal. But if you use Firefox as your only (or even primary) browser, at this point, the only one you’re sticking it to is yourself. I wish it weren’t so, but it is.
Yep, my mistake. I’m not sure either! Math is hard, it seems…
EDIT: That is, I’m not sure how I got 14.85%—that was, like, I pressed the wrong calculator keys, or something. But 60.1% is like this:
(0.3 · 0.005) / ((0.3 · 0.005) + (0.01 · 0.995)) = ~0.60120 = 60.12%
Intuitively it makes sense to me that if someone thinks they got abducted by aliens, it’s more likely they’re hallucinating than that they actually got abducted by aliens. It’s true that aliens actually abducting people wouldn’t mean people stop having hallucinations. But adding P(B|¬A) - the rate of false positives—to P(B|A) - the rate of true positives—seems like some kind of weird double counting. What am I misunderstanding here?
Well, to start with, if you don’t include the false positive rate in P(B|A), and work through the numbers, then, as I said, you’ll find that having the abduction experience will drastically lower your probability estimate of aliens. You would have:
P(A|B) = (0.000005 · 0.01) / ((0.000005 · 0.01) + (0.001 · 0.99)) = 0.00000005 / (0.00000005 + 0.00099) = 0.00000005 / 0.00099005 = ~0.0000505025 = 0.00505025%.
So that’s clearly very wrong—even if it doesn’t tell you what the right answer should be.
But, intuitively… well, I explained it already: if aliens exist and abduct people, some people will still take drugs or go crazy or whatever, and hallucinate being abducted. Bob could be one of those people. It’s not double-counting because the A is “aliens exist and abduct people”, not “Bob was abducted by aliens”. (Otherwise P(A) could not possibly have started as high as 0.01—that would’ve been wrong by many orders of magnitude as a prior!) (This is essentially @clone of saturn’s explanation, so see his sibling comment for more on this point.)
Yeah, I think I described P(A|B) when trying to describe the sensitivity, you are right that whether aliens actually abduct people given Bob experienced aliens abducting him is P(A|B). It’s possible I need to retract the whole section and example.
I agree. But I don’t think that you should discard the text entirely, because it seems to me that there is actually a lesson here.
I have had this experience many times: someone (sometimes on this very website) will say something like, “I know for a fact that X; my experience proves it to me beyond any doubt; I accept that my account of it won’t convince you of X, but I at least am certain of it”.
And what I often think in such cases (but perhaps too rarely say) is:
“But you shouldn’t be certain of it. It’s not just that I don’t believe X, merely based on your experience. It’s that you shouldn’t believe X, merely based on your experience. You, yourself, have not seen nearly enough evidence to convince you of X—if you were being a proper Bayesian about it. Not just my, but your conclusion, should be that, actually, X is probably false. Your experience is insufficient to convince me, but it should not have convinced you, either!”
(This is related to something that Robyn Dawes talks about in Rational Choice in an Uncertain World, when he says that people are often too eager to learn from experience.)
This is also related to what E. T. Jaynes calls “resurrection of dead hypotheses”. If you have an alien abduction experience, then this should indeed raise your probability estimate of aliens existing and abducting people. But it should also raise your probability estimate of you being crazy and having hallucinations (to take one example). And since the latter was much more probable than the former to begin with, and the evidence was compatible with both possibilities, observing the evidence cannot result in our coming to believe the former rather than the latter. As Jaynes says (in reference to his example of whether evidence of psychic powers should make one believe in psychic powers):
…Indeed, the very evidence which the ESPers throw at us to convince us, has the opposite effect on our state of belief; issuing reports of sensational data defeats its own purpose. For if the prior probability of deception is greater than that of ESP, then the more improbable the alleged data are on the null hypothesis of no deception and no ESP, the more strongly we are led to believe, not in ESP, but in deception. For this reason, the advocates of ESP (or any other marvel) will never succeed in persuading scientists that their phenomenon is real, until they learn how to eliminate the possibility of deception in the mind of the reader.
Another error: you have P(ban) = (0.3 · 0.005) + (0.001 · 0.995) but it should be P(ban) = (0.3 · 0.005) + (0.01 · 0.995) (0.001 would be 0.1% false positive rate, not 1% as you stipulate). This results in P(problem|ban) = 14.85% rather than 13.1%.
(Also, I am actually not sure how you got 13.1%. With the aforementioned error, the result would be 60.1%…)
This part is obviously more speculative, but let’s suppose that Bob reasons thus: given that aliens abduct people, there is perhaps an equal chance that they would abduct any human as any other. (Is this a reasonable assumption? Who knows?) And let’s say that they abduct 100 people per year. So the chance of having been abducted at least once in (let’s say) 40 years of life would be 1 − (7,999,999,900 / 8,000,000,000)^40 = ~0.0000005.
Ah, but there’s a catch! The chance of having an abduction experience if there are aliens isn’t just the chance of being abducted, it’s the chance of being abducted plus the chance of falsely coming to believe you’ve been abducted when in fact you have not. (As surely we do not think that the existence of aliens would prevent humans from having schizophrenic episodes or LSD trips etc.?) Thus we must add, to P(B|A), that 0.001 chance of having a false abduction experience, for a total of 0.0010005. (If we didn’t account for this, we’d end up concluding that Bob’s experience should lead him to revise P(A) drastically down!)
So, the revised calculation:
P(A|B) = (0.0010005 * 0.01) / ((0.0010005 * 0.01) + (0.001 * 0.99)) = 0.000010005 / (0.000010005 + 0.00099) = 0.000010005 / 0.001000005 = ~0.01000495 = 1.000495%.
1.000495%. Not 33%. (The prior, we must recall, was 1%.) In other words, this is an update so tiny as to be insignificant.
Of course we can tweak that by modifying our assumptions about the aliens’ behavior—how often do they abduct people, how do they select abductees—but you’d have to start with some truly implausible assumptions to get the numbers anywhere near a large update.
Bob should notice that it is overwhelmingly more likely that his experience was false than that it was real, and it should have essentially no effect whatsoever on his estimate of the probability of the existence of aliens who sometimes abduct people.
He decides the sensitivity of the test—that aliens actually abduct people, given he experienced aliens abducting him—is 5% since he knows he doesn’t have any history of drug use, mental illness, or prankish friends with a lot of spare time and weird senses of humour. (That’s P(B|A).)
Er, what? P(“aliens actually abduct people, given [Bob] experienced aliens abducting him”) is P(A|B), not P(B|A). This is what you’re trying to find out, so it can’t be one of the inputs.
P(B|A), which is indeed the input you want, would be P(“Bob experiences aliens abducting him, given that aliens actually abduct people”). However, this has nothing whatsoever to do with whether Bob has “any history of drug use, mental illness, or prankish friends with a lot of spare time and weird senses of humour”. (It would presumably depend on things like “what is the selection procedure that the aliens use to choose abduction victims”, plus various figures like “how many people are there”, “what is the probability that Bob would be in a certain location at a certain time”, etc., etc.) And I can’t see where you might get a figure of 5% for this.
So, as far as I can tell, the math you provide doesn’t work.
I have used Tiny Tiny RSS and I found it to be good.