How to model the probability of a truth claim given an arrangement of eyewitness accounts supporting specific instances of that claim? Note: the title is adapted from my Philosophy.SE question Epistemic value of multiple eyewitness accounts: single event vs. multiple events given a fixed number of eyewitnesses?. See meta discussion here.

Intuitively speaking, multiple independent eyewitness accounts of a single event are more convincing than a single eyewitness account. For example, multiple independent eyewitness accounts of a loud explosion in a remote area (e.g. from different locations and viewpoints) are more convincing/reliable than a single account (e.g. maybe the single witness hallucinated the explosion).
A bit more formally, if we define X as some truth claim about some event, process or phenomenon in the real world, we could say that:
P(X is true | multiple eyewitness accounts) > P(X is true | a single eyewitness account)
However, what happens if we keep the number of eyewitness accounts constant and only change the number of events?
For example, let X = "alien abductions are real", and let Ei be a concrete example of an (alleged) alien abduction. X is a general claim, Ei is a claim about a very specific instance of X. It is clear that Ei entails X. Thus, which of the following probabilities is greater than the others?

*

*P(E1 is true | N eyewitness accounts for E1)

*P(E1 is true or E2 is true or ... or EN is true | one eyewitness account for Ei, for each i in {1, ..., N})

*P(E1 is true or E2 is true or ... or EN/2  is true | two eyewitness accounts for Ei, for each i in {1, ..., N/2})

*P(E1 is true  or E2 is true or ... or EN/3 is true | three eyewitness accounts for Ei, for each i in {1, ..., N/3})

*Etc.

In other words, given N eyewitness accounts, what is the optimal distribution of eyewitnesses over specific alleged instances of X that maximizes the probability of X being true? What should be more convincing, 1000 eyewitness accounts for E1, 500 eyewitness accounts for E1 + 500 eyewitness accounts for E2, etc.?
Notice that I used eyewitness reports of abductions by aliens as an illustrative example, but the reasoning can be extended to other rare events, such as reports of miracles, paranormal phenomena, angelic encounters, Bigfoot sightings, testimonials from whistleblowers (conspiracy theories), etc.

In my opinion, the most important thing to consider is if there are ways in which eyewitness accounts may not capture the full possibilities of the event (or lack of it), i.e., if they are statistically biased in any way, and if so, how.
Of course, "eyewitness" can be replaced with any non-human objective measurement obtained through a measurement device or procedure, and the question remains whether the measurement is biased or distorted or noisy, and if so, in what way.
A simple example to illustrate the problem is Survivorship bias, i.e., a censored dataset:
Let's assume, for argument's sake, continuing the OP's example, that there indeed are aliens and they abduct humans. But furthermore, let's assume that their abductions are very common, and that the vast majority of the humans being abducted are never returned to Earth. To make matters worse, the aliens can analyze human relationships, and they make an effort to abduct humans with very few relationships and relatives, so as not to draw attention to these missing humans.
In this hypothetical example, there will be zero eyewitnesses of humans abducted and not returned to Earth, even though the assumption is that this is the event with vast majority. The very few cases of abductions of humans which survive to report them is miniscule, obviously in comparison with humans living on Earth which have not been abducted (as far as they're aware...)
So, what would we be able to infer from existing eyewitness accounts if we ignore Survivorship bias?  Probably that the existence of alien abductions is questionable.
However, if we do take take into account the censored dataset caused by Survivorship bias, we would attach non-negligible probability to alien abductions. Of course this is only in the case where we accept this preposterous hypothetical example and attach to it's existence non-zero prior probability...
The example of Survivorship bias of determining reinforcement based on location of bullet holes in the returning aircraft is most illuminating:
https://en.wikipedia.org/wiki/Survivorship_bias#In_the_military
