As an alternative to the 3Blue1Brown video, Arbital has a good post on the odds form of bayes’ theorem.
Also, Microcovid has a good blog post on how to interpret negative test results. In particular, there is some more detailed information on how the sensitivity depends on the number of days it’s been since you’ve been exposed.
I wonder how the delta variant affects all of this.
It seems to me like the most important question is what your prior should start out as. Eg. if you live in this area, develop a 102 degree fever, and have been exposed to roughly 1000 microcovids over the past N days, how likely is it that you have covid? I’d find it really helpful to get some help thinking about those sorts of questions.
I think you get into trouble fairly quickly when trying to ask these questions, and even with some of the parameters already covered by microcovid, due to non-independence and non-linearity of various parameters. E.g. microcovid roughly accounts for the fact that hours of exposure to the same person are not independent exposure events, vs adding more people. But it does that with a hard cap on the number of microcovids you can get from a single person in a single event (IIRC), which is a pretty crude approximation. (Not a single hard numeric cap, but a cap based on the nature of the exposure—I think it’s a good approach, it’s just definitely an approximation of a smoother nonlinear curve that we don’t know how to draw.)
And I don’t think anybody (outside of academic papers in epidemiology) is really accounting for things like the very uneven distribution of spread between people. If almost all spread is from a tiny number of superspreaders, your precautions look very different than if it’s pretty much even across everyone. I think our rough models tend to assume the latter, but the reality is somewhere in between. We mostly hope the various nonlinearities are small or cancel each other out, but I think that’s often not true.
As an alternative to the 3Blue1Brown video, Arbital has a good post on the odds form of bayes’ theorem.
Also, Microcovid has a good blog post on how to interpret negative test results. In particular, there is some more detailed information on how the sensitivity depends on the number of days it’s been since you’ve been exposed.
I wonder how the delta variant affects all of this.
It seems to me like the most important question is what your prior should start out as. Eg. if you live in this area, develop a 102 degree fever, and have been exposed to roughly 1000 microcovids over the past N days, how likely is it that you have covid? I’d find it really helpful to get some help thinking about those sorts of questions.
I think you get into trouble fairly quickly when trying to ask these questions, and even with some of the parameters already covered by microcovid, due to non-independence and non-linearity of various parameters. E.g. microcovid roughly accounts for the fact that hours of exposure to the same person are not independent exposure events, vs adding more people. But it does that with a hard cap on the number of microcovids you can get from a single person in a single event (IIRC), which is a pretty crude approximation. (Not a single hard numeric cap, but a cap based on the nature of the exposure—I think it’s a good approach, it’s just definitely an approximation of a smoother nonlinear curve that we don’t know how to draw.)
And I don’t think anybody (outside of academic papers in epidemiology) is really accounting for things like the very uneven distribution of spread between people. If almost all spread is from a tiny number of superspreaders, your precautions look very different than if it’s pretty much even across everyone. I think our rough models tend to assume the latter, but the reality is somewhere in between. We mostly hope the various nonlinearities are small or cancel each other out, but I think that’s often not true.