Does Faire actually have COVID after testing positive with mild cold-like symptoms?
82%
chance
May 19
M\$621 bet
She woke up with a slight sore throat and took two rapid tests in a row, both positive. Later she developed a slightly runny nose and very occasional cough. Twist: See this market: https://manifold.markets/dreev/do-i-have-covid-despite-testing-neg

Daniel Reeves is betting NO at 48% 13 days ago

Auxiliary market for the preceding question: https://manifold.markets/dreev/does-a-vaccinated-person-with-mild

Daniel Reeves is betting NO at 48% 13 days ago

I suppose if we assume Faire and I have the same virus then our results are kind of like if you got some mild symptoms and took 4 tests in a row and 2 were positive and 2 were negative. How would you Bayesian-update on that?

Daniel Reeves is betting NO at 48% 13 days ago

If we ignore the fact that Faire and I probably have the same virus and just naively apply Bayes' rule for each of us, starting with some prior of having Covid given our symptoms and using the sensitivity/specificity in the pamphlet, we get this for posterior probability as a function of prior probability (blue line is positive test, orange line is negative): https://user-images.githubusercontent.com/9928/168338624-1df49a71-a594-44ff-abbe-d00b2290af96.png So, like, if you got a scratchy throat and slight cough and runny nose and were like "this seems like a 20% chance I have covid" and then you took a rapid test... * if it says positive (like for Faire) then you go from a 20% chance to a 92% chance * if it says negative (like for me) then you go from a 20% chance to a 1.4% chance

Daniel Reeves is betting NO at 48% 13 days ago

Update today: I still have a mild cough but getting better and otherwise feel fine. Faire has been totally fine for days now (today is day 5 for her, with her positive test Sunday being day 0).

Daniel Reeves is betting NO at 48% 13 days ago

I just took another test as well (about 24 hours later) and still negative! My symptoms today: sore throat gone, cough worse (but still not bad), ever so slightly headachy I guess but mostly pretty normal. Runny nose pretty much better, but was only ever very minor. I'm day 2 or 3. (Tuesday I had an inkling I was getting sick, Wednesday was the first day of actual symptoms, though still very mild.)

Daniel Reeves bought M\$88 of NO13 days ago

The antigen rapid test pamphlet says sensitivity ie Pr(pos | covid with symptoms) = 33/35 and specificity ie Pr(neg | not covid but yes symptoms) = 102/104

brp is betting YES at 48% 13 days ago

@dreev These numbers aren't enough to derive anything solid about your position, but having reviewed https://www.lesswrong.com/posts/cEohkb9mqbc3JwSLW/how-much-should-you-update-on-a-covid-test-result, I think I invested *much* too aggressively.

Daniel Reeves is betting NO at 48% 13 days ago

@brp Ah, thanks for that link! We're using the "iHealth COVID-19 Antigen Rapid Test" which isn't mentioned there. And of course the other confusing monkey wrench in our calculation is Faire testing positive but me testing negative with the same symptoms.
@dreev I'd probably use the average stats for all rapid tests, I suspect that most rapid tests are in the same rough ballpark. I also commented on the other market about this https://manifold.markets/dreev/does-a-vaccinated-person-with-mild - you should ignore the pamphlet stats, apparently they are completely bogus because the sample for them is highly infectious individuals (chosen to make the statistics pass arbitrary regulatory standards) - that's why it comes out with such a high sensitivity rate compared to the meta-review.

Daniel Reeves is betting NO at 93% 13 days ago

Ha, Faire just took another test, day 4, and it's negative!

brp is betting YES at 48% 13 days ago

@dreev Good for her! I hope it's just allergies, but I still kind of doubt it..
Very good question. It's entirely possible we won't get a definitive answer and will have to resolve it as either "N/A" or resolve to the market's own probability. We can commit to updating this thread with all the new information we have.

brp bought M\$100 of YES14 days ago

How does this market resolve? A PCR test? More rapid tests? Worse symptoms?