I find it helpful to have more real world examples to anchor on so here’s another COVID-related example of what I’m pretty sure is likelihood / probability confusion.
Sensitivity and specificity (terrible terms IMO but common) model Pr(positive test∣I have COVID) and Pr(negative test∣I don't have COVID) respectively and therefore are likelihoods. If I get a positive test, I likely have COVID, but it still may not be very probable that I have COVID if I live in, e.g. Taiwan, where the base rate of having COVID is very low.
I find it helpful to have more real world examples to anchor on so here’s another COVID-related example of what I’m pretty sure is likelihood / probability confusion.
Sensitivity and specificity (terrible terms IMO but common) model Pr(positive test∣I have COVID) and Pr(negative test∣I don't have COVID) respectively and therefore are likelihoods. If I get a positive test, I likely have COVID, but it still may not be very probable that I have COVID if I live in, e.g. Taiwan, where the base rate of having COVID is very low.