You so-called skeptics do not have the mental capacity to calculate that the universe does not give a damned about your opinion about what is "weird" or "extraordinary".

For your information, the only way to really settle anything about "proof" in the physical world is to get computers to do Artificial Intelligence. The computer does not give a
s*** how dumbass humans categorize events. A computer has no prior knowledge to
put ONE event into the category with ANOTHER event. ALL the computer with AI sees is
a bunch of PIXELS moving about.

Start with that. Then draw conclusions based upon LOGICAL CONSISTENCY
of the motion of OTHER pixels. THAT is what NEEDS to be done!

Here is where you so-called skeptics never do mathematical modelling:
Event A) If a security video camera in a bank takes images, and those images look like a person robbing a bank, then we conclude that a person is robbing a bank.
Event B) If a video camera takes images of something that looks like intelligently
controlled craft, then we conclude that there are intelligently controlled craft.
(Extend this to capturing an alien on film.)

If B is false, then A is false. Contrapositively, if A is true, then B must be true.
The SAME level of PROOF MUST APPLY, because HARD PROOF and THE UNIVERSE DON'T GIVE A F**** DAMN WHAT the video camera takes pictures of !!

I am a proud American Atheist who also believes the Alien Hypothesis for many UFOs.
I believe there is no god and that aliens do visit our planet, somehow, in the same way I believe the Goldbach Conjecture is true, the same way you might believe there is a god, that aliens are not causing many of the UFOs, and that the Goldbach Conjecture is false.
In all three cases, we have no proof in either direction. However, I can make an logically consistent decision by considering:

1) The Center for Cell Biology in Washington state demonstrated via massive calculations, involving setting many numerical parameters of protein synthesis pathways in various combinations, that life could have formed in all its current complexity WITHOUT any formal "design". Conclusion: there is no god.

2) Thousands of INDEPENDENT sightings of things that LOOK like controlled craft and ACT like controlled craft, also associated with aliens -- so why not call it a craft? Not to mention a few sightings of the creatures themselves. Conclusion:
these craft are intelligently controlled by aliens.

3) Every even number so far tested is the sum of two odd primes.
Conclusion: all even numbers are the sum of two odd primes.

Here is where the mathematical logic comes in.

If the statistical evidences for the conclusions of 2 is not sufficient to reasonably draw its conclusions, then neither is 1 nor 3. Contrapositively, if we can reasonably make the conclusions for 1 or 3, then the same must be true for 2.

Now, if you say, formal logic does not apply across different "aspects" or "realms" of the universe, then it applies across none, INCLUDING and ESPECIALLY HOW YOU and I choose to categorize the universe. One event on 2007 May 15 that you call a "UFO sighting" is just as different an event to a "UFO sighting on 2007 May 22" as it is to "terrorist attacks on 9/11"
once you declare "logic does not apply".
Everything follows once you say "logic does not apply".

FYI: I have a PhD and MS in Mathematics, Rutgers University, and BChE
(Bachelor of Chemical Engineering) degree, U of Delaware.
I have personally NEVER seen ANY anomalous objects in the sky which I would deem
"alien". Neither have I seen Iraq in person.