[FRIAM] From My Former Colleague

[Frank Wimberly]

Who wrote a widely cited paper with the title Why I am Not a Bayesian.

"I have not found on the web any calculation of the probability that you
have covid given that you have just decided to take a home covid antigen
test and found a positive result.  So I did a couple.

Abbott Laboratories Rapid antigen covid test (the only one I could get real
numbers for):

"The BinaxNOW test correctly gave a positive result 84.6% of the time
compared to PCR. In the same study, the test correctly gave a negative
result 98.5% of the time."

I will assume that PCR results are ground truth. Assume the base rate of
covid infection is 5%--the frequency of infectious covid among people you
have come in contact with in the last several days.  Applying Bayes Theorem:

pr(covid | positive test) = .05 pr(positive test | covid) / pr(positive
test) =

.05 x .846 / (pr (positive test | covid) pr(covid) + pr(positive test | no
covid) pr(no covid)) =

.0423 / (.846 x .05 + .15 x .95)  = .0423 / (.0423 + .1425) = .0423 / .1848
= .2288

If the base rate of covid infection is 10% the probability of covid given a
positive test is

.0846 / .0846 +.135 = .3852.

Bayes say you probably don't have covid. Moral: don't worry but quarantine
until you get a negative PCR result."


---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505

505 670-9918
Santa Fe, NM
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