Help me with bayesian thinking re:coronavirus?

post by hereisonehand · 2020-03-08T17:03:23.320Z · score: 6 (3 votes) · LW · GW · No comments

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If I have a fever, what is the likelihood that I have a coronavirus infection? I'm actually less interested in the answer than in the underlying thought process, so feel free to insert variables where reliable numbers are hard to find.

I'm just having trouble thinking clearly about this. Do I start with the prevalence of coronavirus and adjust that base rate by saying if I have a fever, the probability goes up because 99% of coronavirus cases have a fever? I guess I could also start with the % of fevers that are due to respiratory conditions as my base rate. And then compare the proportion of respiratory-related fevers from coronavirus to other causes?

I'm having trouble because I realize that lots of common non-coronavirus conditions cause a fever, and that if I have a fever, the probability I have coronavirus has increased, but I can't figure out how to clearly convert the relevant information into a series of mathematical statements. This feels like a very practical exercise of bayesian thinking, so I would love to see how people who are more fluent than I am with this kind of reasoning would approach this problem.

Thanks!

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answer by alahonua · 2020-03-08T18:01:08.453Z · score: 6 (4 votes) · LW(p) · GW(p)

To answer properly you need to know the prevalence of fever of any kind. In particular, you might use the number of days with fever per year you had last year / 365, for example. If you literally never get a fever for years, I'd worry more then if you did.


P(19coro | fever) = P(fever| 19coro, about 0.5??) * P(19coro, perhaps 0.001??) / P(fever)

comment by Bucky · 2020-03-08T21:21:55.316Z · score: 4 (2 votes) · LW(p) · GW(p)

Just for clarification P(fever) must include fever which comes from 19coro.

comment by alahonua · 2020-03-09T06:38:55.501Z · score: 3 (2 votes) · LW(p) · GW(p)

Yes, true. The exact numbers are very uncertain, but the qualitative point remains that someone who feels fever many days per winter has less chance of a similar day with fever being from covid than someone with a fever today who has had no fever for over a year.

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