[mikorym]

I appreciate all the answers that point out Bayes's theorem. One thing to add is that in contrast to the usual classroom Bayes the "occurrence in the general population" is very much a variable rather than a constant. For example, Germany's low death rate can be a side effect of the false positive issue in the paper.

In fact, the stark difference between Italy and Germany would provide support to the paper's conclusion.

[eveningcoffee]

There can be other explanation for this difference http://www.savespain.eu/italy-vs-germany because there is huge disparity between Italy and Germany infected population demographic.

My hypothesis is that this comes from bigger inter-generation connections in Italy.

[astrophysician]

Right, so it's a variable, but if we can independently nail down a false negative/positive rate, then we could try to infer the true rate of infection, but problem is (assuming US numbers):

* assume false positive rate of 10%, assume true positive rate of 100% (it's not but let's be generous)

* maybe 1/10 of the population (30 million) gets tested

* lets say 100,000 people have COVID right now (50x the official number)

number of positive tests = 30 million * 0.1 + 100k * 1 = 3,100,000

fraction of postive tests that actually have the disease = 1 / 31 = 3.2%

problem is FPR (1) depends on the population tested (i.e. p(covid | positive test) != p(covid|positive test, some symptoms) != ...), (2) we need very accurate measurements of FPR because:

lets say we constrain FPR to 10% +/- 1% ==> 10% uncertainty in FPR -- that means our inference of the number of infected people is:

n_infected = (n_positive_tests - FPR * n_tested)

which is: -200,000 to 400,000

so...not very useful.