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The Jeffrey posterior in the answer is closed form and Bayesian. The other answer is a profile likelihood. Neither involve Monte Carlo sampling. Both are gener
by usgroup 1y ago
The Jeffrey posterior in the answer is closed form and Bayesian. The other answer is a profile likelihood.
Neither involve Monte Carlo sampling. Both are general and principled.
- bjornsing 1y agoThe answer looks a bit simplistic compared to the question (as I interpreted it at least). In order to estimate the risk of incorrect ordering you have to calculate P(p2 > p1) where p1 and p2 are drawn from different beta distributions. AFAIK there’s no closed form expression for that probability (so Monte Carlo is one possible approach).
- usgroup 1y agoThe question doesn’t ask for that —- it explicitly asks us to control for over estimation of the fraction — although I rather like your interpretation as an extension.
- bjornsing 1y agoOk. I may have read a bit too much into this paragraph: > Order the items above, smallest fraction first, whilst taking into account the uncertainty in the number of trials to bound the probability of over-estimating each fraction. But why mention ordering if you’re not looking for statistical reasoning around the ordering in particular?