God, Santa, and The Tooth Fairy

[R00tKiT]

I can understand a conception of god that inherently disqualifies god from the category of ‘magical, imaginary things,’ i.e. the tooth fairy, Santa Clause, etc. (thank you @Neo-Scholastic for harping on the subject often enough that it finally tickled my thinker), and I’m happy to be charitable toward any argument that attempts to make such a distinction. What I’m having a hard time with is.

Let's take a much simpler assertion than God's existence;

P: "LadyForCamus is a real person".

How would you go about proving P to someone who doesn't personally know you? 

You could think of sending them pictures of yourself, but this only proves a woman exists where you live, not that she's specifically LadyForCamus. You could think of pointing out to everything you wrote about this forum. But your account could very well be a sophisticated AI, although this is a stretch, it can't be clearly ruled out. You could think of presenting legal documents with your full name and your picture. This can still be insufficient to a hardcore skeptic. After all, criminals falsify these documents all the time and may even create a fictional person to cover their illegal activity etc.

I think you would agree with me by now that it's really hard to prove P, and at the same time, nobody here has any problem accepting P and even take anything you say about LadyForCamus at face value.

P is an existential assertion, just like the assertion of theism, or that of Santa Claus's existence, etc. This kind of assertion can't be proven through deductive arguments, because LadyForCamus has to be in the premises, and the premises should be some very general fact about the world that no one can reasonably dispute.
Except that, there is no general fact about the world that points to anyone's name or identity, let alone existence.

We are then left with inductive reasoning. I already tried many times in this forum to explain the relevance of induction to discussions about theism, and maybe I wasn't clear enough.
I suggest we look at it from a different and well-known scientific approach: that of statistical inference. 

Let's consider the null hypothesis 

H0 : "There is no sufficient evidence LadyForCamus exists". 

As opposed to the alternative hypothesis :

H1 (which is the assertion P as above) : "LadyForCamus definitely exists".

Now consider the following evidence under H0 : all your pictures, everything you wrote in this forum and elsewhere, you own insistance that you really are LadyForCamus, etc.
All this evidence is highly unlikely under H0, it's unlikely that's someone will make up all this stuff consistenly and for a very long period.

It's precisely the fact that the evidence is surprising under H0 that proves your existence. 

We quantify this (((level of surprise))) by the so-called p-value, the smaller the p-value, the more surprising is the evidence under H0. If the p-value is smaller than some predefined probability, then we can reasonably reject H0 and accept that you exist. The skeptic can always tinker with the evidence and claim it's not surprising, there is always a way to avoid P. It's the same thing when a theist attempts to prove God exists. We take all available the information about fine-tuning, the complexity of life forms, etc. and assess whether they are surprising under H0 (naturalism/a world without a personal creator). But the skeptic can always lift his epistemic requirements arbitrarily and claim that none of thus stuff is surprising, there is always a way out.

I may have butchered some statistical concepts along the way, but I hope the idea is clear.