[ExI] The Chinese bullshit theorem

[Stuart LaForge]

Claim:
The novel coronavirus most likely came from the lab in Wuhan.

Let L be the hypothesis that nCoV19 came from a lab.
Let M, for market, be the hypothesis that nCoV19 came about by chance  
evolution in a wet market of mixed live animals.
Let W be the observation that the virus arose in Wuhan, China.

By Bayes’ Theorem, the likelihood or posterior probability that the  
coronavirus originated in the lab given that the initial outbreak  
happened in Wuhan is P(L|W)  =  P(W|L)P(L) /(P(W|L)P(L) + P(W|M)P(M)).

Similarly the likelihood that the coronavirus originated in the wet  
market given that the initial outbreak happened in Wuhan is P(M|W)  =   
P(W|M)P(M) /(P(W|L)P(L) + P(W|M)P(M)).

In order to find likelihood ratios for the two hypotheses we simply  
divide their likelihoods

P(L|W)  /P(M|W) =[ P(W|L)P(L) /(P(W|L)P(L) + P(W|M)P(M))]/ [P(W|M)P(M)  
/(P(W|L)P(L) + P(W|M)P(M))].

The denominators are equal, so they cancel out to give us a likelihood ratio:

R := P(L|W) /P(M|W)  =P(W|L)P(L)/( P(W|M)P(M))

Now we just need to assign our probabilities. If the virus came about  
because of random evolution in the wet market, then it could have  
evolved in any wet market in China. Since wet markets have been part  
of Chinese culture for centuries, every city in China has a wet  
market. There are 686 cities in China and therefore 686 wet markets.   
That means that the probability that the outbreak happened in Wuhan  
given that the coronavirus came from a wet market is 1/686.

P(W|M) = 1/686

On the other hand, there is only one biosafety level 4 virus lab in  
all of China and it is in Wuhan. Therefore, the probability that the  
outbreak happened in Wuhan, given that the virus came from the lab is 1.

P(W|L) = 1

If we start with an assumption that either scenario is equally  
probable, then P(L) = P(M) and so they cancel out, giving us a  
likelihood ratio

R = P(W|L)/P(W|M)  = 1/(1/686) = 686.

Or in other words, given uninformative unbiased priors, Bayes theorem  
demonstrates that it is 686 times more likely that the novel  
coronavirus that causes COVID-19 came from the lab in Wuhan rather  
than from the wet market there.

Q.E.D.

Note that even if you assign the wet market story a prior probability  
of .95, Bayes still says that the lab hypothesis is still 36.1 times  
more likely.

Stuart LaForge