In practice it's simply impractical to incorporate every potentially relevant observation into our thinking. But that makes it awfully easy to have some bias in selection, and that can make a huge difference to the conclusions.
Yes these circumstances induce bias and this is unfortunate if one wants to say anything about frequency and such things.
Another somewhat simpler question is this: given n observations of something the observer thinks is a UAP, what is the probability that at least one of these observations originated from a UAP?
If for each of these observations P( observation | UAP ) is strictly greater than 0, then I suspect P(UAP) will go towards 1, monotonously, as the number of observations increases.
Is this hunch somewhat correct? How do I express this hunch mathematically..?
I also touch on this question in the section 'Future work' in my article, but I don't have the answer.
If for each of these observations P( observation | UAP ) is strictly greater than 0, then I suspect P(UAP) will go towards 1, monotonously, as the number of observations increases.
No. This violates the law of conservation of expected evidence. The relevant question is whether P( observation | UAP ) is bigger or smaller than P( observation | ~UAP ).
The problem, as I mentioned above, is that it's hard to estimate P( observation | UAP ).
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?