"You cannot use confidence intervals to argue the validity of a point estimate inside of the CI."
You're using a Bayesian method, so you have a posterior distribution. You can sample from it.
"And no, just because 1.5% is in the 95th percentile of the posterior prevalence, does not mean you can say that 1.5% is a valid estimate."
You told me that was the confidence interval on the parameter. The confidence interval contains the point estimate for the original study. It's as valid as any other point within the confidence interval. As you say: "you cannot use confidence intervals to argue the validity of a point estimate inside the CI".
"What the CI shows is that, with 97% confidence, the prevalence is somewhere between -0.3% and 1.7%."
> You told me that was the confidence interval on the parameter. The confidence interval contains the point estimate for the original study. It's as valid as any other point within the confidence interval. As you say: "you cannot use confidence intervals to argue the validity of a point estimate inside the CI".
> Which includes 1.5%.
And everything else in the CI. If we're treating this like a CI, then it's like saying a dice will land on 1, just because it's equally likely to land on 6.
The actual P(1.5% | prevalence) is quite low at 3%.
"And everything else in the CI. If we're treating this like a CI, then it's like saying a dice will land on 1, just because it's equally likely to land on 6. The actual P(1.5% | prevalence) is quite low at 3%."
You just said that you can't use a CI to estimate the likelihood of any point within the CI (you actually can, for well-behaved problems, but I digress) when I commented that 0% isn't a likely outcome within the interval.
Literally the same argument. If you want to argue that 1.5% is unlikely, then you have to accept that 0% is unlikely for the same reasons.
You're using a Bayesian method, so you have a posterior distribution. You can sample from it.
"And no, just because 1.5% is in the 95th percentile of the posterior prevalence, does not mean you can say that 1.5% is a valid estimate."
You told me that was the confidence interval on the parameter. The confidence interval contains the point estimate for the original study. It's as valid as any other point within the confidence interval. As you say: "you cannot use confidence intervals to argue the validity of a point estimate inside the CI".
"What the CI shows is that, with 97% confidence, the prevalence is somewhere between -0.3% and 1.7%."
Which includes 1.5%.