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I don't think you can do this. You have a reasonably good upper bound of the probability, but you don't have any justification for putting any lower bound other
by gweinberg 8y ago
I don't think you can do this. You have a reasonably good upper bound of the probability, but you don't have any justification for putting any lower bound other than zero on the probability.
In particular, if you're considering the probability of a catastrophic event, it's probably better to find some other rationale for estimating the probability than just saying 'it has never happened before'.
- carlmr 8y agoExactly, the maximum likelihood estimator given your data is 0. You can just have a looser or stricter upper bound, depending on your requirements. However without a better model of your distribution and/or better priors (experience), you won't get a tighter estimate.