Confidence intervals over probabilities don’t make much sense to me. The probability itself is already the confidence interval over the binary domain [event happens, event doesn’t happen].
I guess to me the idea of confidence intervals over probabilities implies two different kinds of probabilities. E.g., a reducible flavor and an irreducible flavor. I don’t see what a two-tiered system of probability adds, exactly.
This was an extensive debate in the 1980s and 90s between Judea Pearl, Dempster-Schafer, and a few others. I think it’s trivially true, however, that in the probability centric view you espouse, it can be helpful to track second order uncertainty, and reducible versus irreducible uncertainty is critical for VoI analysis.
And for more on the debates about second-order probabilities and confidence intervals, and why Pearl says you don’t need them, you should just use a Bayesian Network, see his paper here: https://core.ac.uk/download/pdf/82281071.pdf
Confidence intervals over probabilities don’t make much sense to me. The probability itself is already the confidence interval over the binary domain [event happens, event doesn’t happen].
I guess to me the idea of confidence intervals over probabilities implies two different kinds of probabilities. E.g., a reducible flavor and an irreducible flavor. I don’t see what a two-tiered system of probability adds, exactly.
This was an extensive debate in the 1980s and 90s between Judea Pearl, Dempster-Schafer, and a few others. I think it’s trivially true, however, that in the probability centric view you espouse, it can be helpful to track second order uncertainty, and reducible versus irreducible uncertainty is critical for VoI analysis.
What is Vol analysis?
Value of Information
Here’s my brief intro post about it:
https://forum.effectivealtruism.org/posts/8w2hNT5WtDMzoaGuy/when-to-find-more-information-a-short-explanation
And for more on the debates about second-order probabilities and confidence intervals, and why Pearl says you don’t need them, you should just use a Bayesian Network, see his paper here: https://core.ac.uk/download/pdf/82281071.pdf