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Now this is an interesting abuse of Bayes' theorem, because there's an extremely similar conspiracy theory going around in China of this form: it's known that C

by knzhou 7y ago

Now this is an interesting abuse of Bayes' theorem, because there's an extremely similar conspiracy theory going around in China of this form: it's known that CIA agents specifically visited Wuhan before the virus broke out, and the CIA claims to have known about this disease before anybody in China did. So... P(virus from CIA) = 0.01 P(outbreak in 14km radius | virus from CIA) = 1 P(outbreak in 14km radius | virus not from CIA) = 1/3,000 Then Bayes' rule gives P(virus from CIA | outbreak in 14km radius) ~= 97%. But wait a second! How can there both be a 97% chance that the CIA did it, and a 97% chance that WIV made it? The reason is that both of these calculations are total bullshit.

dlubarov 7y ago
What do you mean by P(virus from CIA)? Do you mean the probability that the CIA planted the virus in the WIV? If so, then > How can there both be a 97% chance that the CIA did it, and a 97% chance that WIV made it? There's no contradiction there. If the CIA planted the virus in the WIV, then it's simultaneously true that the CIA planted the virus and that the WIV was the source of the outbreak.
- knzhou 7y ago
  Why not both? Using your exact logic three times: - there's a 97% chance the CIA planted it in the seafood market - there's a 97% chance the CIA planted it in the WIV - there's a 97% chance the WIV made it Now it's obvious that something is going wrong here. There is no conceivable way these probability assignments can make sense. But your math was formally correct! What a mystery.
  - dlubarov 7y ago
    I threw out 1% as a seemingly reasonable prior probability that the outbreak came from the WIV, given an implicit assumption that the virus originated in China. Obviously I didn't put much thought into the exact number, but 1% seems within the realm of reason to me, given that the WIV is the only BSL-4 facility in China. It doesn't make sense to apply the same prior to "the CIA planted COVID-19 in the Huanan Seafood Wholesale Market", because there are many such markets in China, and only one BSL-4 facility. You might think 1% is a reasonable prior for "the CIA planted COVID-19 in some market in China", but then it wouldn't make sense to adjust the probability based on the outbreak location as I did. What you're doing is like starting with a prior probability of 10% that a random individual lives in Maui, and 10% that a random individual lives in Kawaii. Then you learn that an individual lives in Hawaii, and you try to adjust both probabilities based on Hawaii's population in relation to the world population. Bayes' theorem gives ~99.8% each for P(Maui | Hawii) and P(Kawaii | Hawaii). The results are obviously impossible, but the argument wasn't structurally wrong, you just started with bad priors. You should have started with P(Kawaii) ~= 0.001%, giving P(Kawaii | Hawaii) ~= 5%, which is correct.
    - knzhou 7y ago
      > It doesn't make sense to apply the same prior to "the CIA planted COVID-19 in the Huanan Seafood Wholesale Market", because there are many such markets in China, and only one BSL-4 facility. I didn't make an error. The way the conspiracy theory goes in China is that the Military World Games [0] were held in Wuhan just before the outbreak. In other words, they knew the US military was in Wuhan specifically (in fact, right next to the seafood market), just like you know that WIV is in Wuhan specifically. The two conspiracy theories really are equally credible, by which I mean they're both bullshit. The reason is because of this assumption you made: P(my favorite conspiracy theory) = 0.01 P(outbreak in 14km radius | my favorite conspiracy theory is false) = 1/3,000 Because 1/3000 is so much lower than 1/100, you're essentially assuming from the start that your favorite conspiracy theory (insert "WIV" or "CIA" or whatever else here) is a much better explanation than all other possible explanations combined, because all of them combined can only total up to a likelihood of 1/3000. In other words, you rigged the game to support your conspiracy theory from the start. I was trying to point out how similar rigging can be used to justify any conspiracy theory. 0: https://en.wikipedia.org/wiki/2019_Military_World_Games https://en.wikipedia.org/wiki/2019_Military_World_Games
      - dlubarov 7y ago
        Yes, I assumed that if the virus is not from the WIV, then all areas of China (weighted by population) would be equiprobable candidates for the outbreak location. Of course this is an imperfect model, but I think it's a reasonable one. This alternate conspiracy seems way more farfetched to me (why would US intelligence need such any such event to get an agent into China?), but if someone believed that it should be given a non-negligible prior, then they should revise my assumption that > P(outbreak in 14km radius | virus not from WIV) = 1/3,000 I.e. their revised value should be at least as large as their prior for the alternate conspiracy. What part of the argument are you disputing exactly? Are you claiming that applying Bayes' theorem in this way is somehow invalid, or are you just taking issue with the assumption quoted above?
        gabaix 7y ago
        Thanks for using Bayes theorem. Although it does not provide evidence, it should guide us to where we should look for evidence. I am also very surprised at people throwing probabilistic equivalence between foreign-agent conspiracy, and an accident in a lab. It seems that the latter is so much more probable.

by knzhou 7y ago

dlubarov 7y ago

What do you mean by P(virus from CIA)? Do you mean the probability that the CIA planted the virus in the WIV? If so, then > How can there both be a 97% chance that the CIA did it, and a 97% chance that WIV made it? There's no contradiction there. If the CIA planted the virus in the WIV, then it's simultaneously true that the CIA planted the virus and that the WIV was the source of the outbreak.

knzhou 7y ago
Why not both? Using your exact logic three times: - there's a 97% chance the CIA planted it in the seafood market - there's a 97% chance the CIA planted it in the WIV - there's a 97% chance the WIV made it Now it's obvious that something is going wrong here. There is no conceivable way these probability assignments can make sense. But your math was formally correct! What a mystery.
- dlubarov 7y ago
  I threw out 1% as a seemingly reasonable prior probability that the outbreak came from the WIV, given an implicit assumption that the virus originated in China. Obviously I didn't put much thought into the exact number, but 1% seems within the realm of reason to me, given that the WIV is the only BSL-4 facility in China. It doesn't make sense to apply the same prior to "the CIA planted COVID-19 in the Huanan Seafood Wholesale Market", because there are many such markets in China, and only one BSL-4 facility. You might think 1% is a reasonable prior for "the CIA planted COVID-19 in some market in China", but then it wouldn't make sense to adjust the probability based on the outbreak location as I did. What you're doing is like starting with a prior probability of 10% that a random individual lives in Maui, and 10% that a random individual lives in Kawaii. Then you learn that an individual lives in Hawaii, and you try to adjust both probabilities based on Hawaii's population in relation to the world population. Bayes' theorem gives ~99.8% each for P(Maui | Hawii) and P(Kawaii | Hawaii). The results are obviously impossible, but the argument wasn't structurally wrong, you just started with bad priors. You should have started with P(Kawaii) ~= 0.001%, giving P(Kawaii | Hawaii) ~= 5%, which is correct.
  - knzhou 7y ago
    > It doesn't make sense to apply the same prior to "the CIA planted COVID-19 in the Huanan Seafood Wholesale Market", because there are many such markets in China, and only one BSL-4 facility. I didn't make an error. The way the conspiracy theory goes in China is that the Military World Games [0] were held in Wuhan just before the outbreak. In other words, they knew the US military was in Wuhan specifically (in fact, right next to the seafood market), just like you know that WIV is in Wuhan specifically. The two conspiracy theories really are equally credible, by which I mean they're both bullshit. The reason is because of this assumption you made: P(my favorite conspiracy theory) = 0.01 P(outbreak in 14km radius | my favorite conspiracy theory is false) = 1/3,000 Because 1/3000 is so much lower than 1/100, you're essentially assuming from the start that your favorite conspiracy theory (insert "WIV" or "CIA" or whatever else here) is a much better explanation than all other possible explanations combined, because all of them combined can only total up to a likelihood of 1/3000. In other words, you rigged the game to support your conspiracy theory from the start. I was trying to point out how similar rigging can be used to justify any conspiracy theory. 0: https://en.wikipedia.org/wiki/2019_Military_World_Games https://en.wikipedia.org/wiki/2019_Military_World_Games
    - dlubarov 7y ago
      Yes, I assumed that if the virus is not from the WIV, then all areas of China (weighted by population) would be equiprobable candidates for the outbreak location. Of course this is an imperfect model, but I think it's a reasonable one. This alternate conspiracy seems way more farfetched to me (why would US intelligence need such any such event to get an agent into China?), but if someone believed that it should be given a non-negligible prior, then they should revise my assumption that > P(outbreak in 14km radius | virus not from WIV) = 1/3,000 I.e. their revised value should be at least as large as their prior for the alternate conspiracy. What part of the argument are you disputing exactly? Are you claiming that applying Bayes' theorem in this way is somehow invalid, or are you just taking issue with the assumption quoted above?
      - gabaix 7y ago
        Thanks for using Bayes theorem. Although it does not provide evidence, it should guide us to where we should look for evidence. I am also very surprised at people throwing probabilistic equivalence between foreign-agent conspiracy, and an accident in a lab. It seems that the latter is so much more probable.