I hadn’t actually read the review, but yes I meant that the sample must have had 29 people who were known (through other means) to be positive for SARS-cov-2, and all tested positive.
Can you say more about how you got 96%?
Educated guessing, really. I did a few simple models with a spreadsheet for various prior probabilities including some that were at each end of being (subjectively, to me) reasonable. Only the prior for “this study was fabricated from start to finish but got through peer review anyway” made very much difference in the final outcome. (If you have 10% or more weight on that, or various other “their data can’t be trusted” priors then you likely want to adjust the figure downward)
So with a rough guess at a prior distribution, I can look at the outcomes from the point of view of “what single value has the same end effect on evidence weight as this distribution”. I make it sound fancy, but it’s really just “if there was a 30th really positive test subject in these dozen or so possible worlds that I’m treating as roughly equally likely, and I only include possible worlds where the validation detected all of the first 29 cases, how often does that 30th test come up positive?” That come out at close to 96%.
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 hadn’t actually read the review, but yes I meant that the sample must have had 29 people who were known (through other means) to be positive for SARS-cov-2, and all tested positive.
Educated guessing, really. I did a few simple models with a spreadsheet for various prior probabilities including some that were at each end of being (subjectively, to me) reasonable. Only the prior for “this study was fabricated from start to finish but got through peer review anyway” made very much difference in the final outcome. (If you have 10% or more weight on that, or various other “their data can’t be trusted” priors then you likely want to adjust the figure downward)
So with a rough guess at a prior distribution, I can look at the outcomes from the point of view of “what single value has the same end effect on evidence weight as this distribution”. I make it sound fancy, but it’s really just “if there was a 30th really positive test subject in these dozen or so possible worlds that I’m treating as roughly equally likely, and I only include possible worlds where the validation detected all of the first 29 cases, how often does that 30th test come up positive?” That come out at close to 96%.
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!