I’m having trouble discerning this from your description and I’m curious—is this approach closely related to the approach GWS describes above, involving the beta distribution, which basically seems to amount to adding one “phantom success” and one “phantom failure” to the total tally?
It is related in the sense that if your prior for sensitivity is uniform, then the posterior is that beta distribution.
In my case I did not have a uniform prior on sensitivity, and did have a rough prior distribution over a few other factors I thought relevant, because reality is messy. Certainly don’t take it as “this is the correct value”, and the approach I took almost certainly has some major holes in it even given the weasel-words I used.
I’m having trouble discerning this from your description and I’m curious—is this approach closely related to the approach GWS describes above, involving the beta distribution, which basically seems to amount to adding one “phantom success” and one “phantom failure” to the total tally?
It is related in the sense that if your prior for sensitivity is uniform, then the posterior is that beta distribution.
In my case I did not have a uniform prior on sensitivity, and did have a rough prior distribution over a few other factors I thought relevant, because reality is messy. Certainly don’t take it as “this is the correct value”, and the approach I took almost certainly has some major holes in it even given the weasel-words I used.
Thanks for the info!