Going outside the argument, if you come up with 50% chance that any given observation of a UAP was actually observing a UAP, you've done something wrong.
This percentage is conditional on P( observation | UAP ) being high (0.8). I guess only a minority of such observations (if any) are that high.
Didn't click through to the study, but what is an 'observation' in this case? I make 3200 observations a day, but I don't observe 70 UAPs a day. It seems far more likely that this was 3200 instances of someone reporting a UAP - in other words, the 22% is pointing towards P(UAP|UO), not P(UAP). But "we couldn't identify this" doesn't necessarily mean it was a UAP, so this is still an overestimate.
If this is so, then I can't use any empirical study to estimate P( UAP ). What value should I then guesstimate P( UAP ) to be? If I choose a generic 0.5, then the result will be an even higher P( UAP | observation ) than 0.53. Thus it would be even harder to dismiss the observation.
If I instead make my own estimation, say, 0.0000001, then one could ask if this was still an epistemologically sound approach. My choice would be rather arbitrary.
Previously we decided P(UO1|UAP) to be 0.8 [...] Thus P(UO1|¬UAP) must be 1−0.8=0.2
No.
Could you elaborate?
Thanks for your feedback :)
If you don't have an epistemically sound approach, then you should probably say "I don't know" instead of using an epistemically unsound one, or at least say "this is really bad, and you shouldn't put high confidence in my conclusions, but it's the best I can do, so..."
That said, one option you have is not to calculate P(UAP) at all, and instead calculate a likelihood ratio:
P(UAP|UO1) / P(¬UAP|UO1) = P(UO1|UAP) / P(UO1|¬UAP) × P(UAP)/P(¬UAP)
So if you just calculate P(UO1|UAP) / P(UO1|¬UAP), then anyone can update their P(UAP) appropriat...
It would be a powerful tool to be able to dismiss fringe phenomena, prior to empirical investigation, on firm epistemological ground.
Thus I have elaborated on the possibility of doing so using Bayes, and this is my result:
Using Bayes to dismiss fringe phenomena
What do you think of it?