Reflecting, in the everything-is-Gaussian case a prior doesn’t help much. Here, your posterior mean is a weighted average of prior and likelihood, with the weights depending only on the variance of the two distributions. So if the likelihood mean increases but with constant variance then your posterior mean increases linearly. You’d probably need a bias term or something in your model (if you’re doing this formally).
This might actually be an argument in favour of GiveWell’s current approach, assuming they’d discount more as the study estimate becomes increasinly implausible.
I agree.
Reflecting, in the everything-is-Gaussian case a prior doesn’t help much. Here, your posterior mean is a weighted average of prior and likelihood, with the weights depending only on the variance of the two distributions. So if the likelihood mean increases but with constant variance then your posterior mean increases linearly. You’d probably need a bias term or something in your model (if you’re doing this formally).
This might actually be an argument in favour of GiveWell’s current approach, assuming they’d discount more as the study estimate becomes increasinly implausible.