That's the same method I use, except that I also include other people's experiences. For example, I've personally never tried jumping off a bridge; but I am reluctant to try this, since, based on what I know of biology, physics, and, indeed, attempts to do so by other people, I know that the experience will likely be fatal.

At the moment I, too, am reluctant to try jumping off a bridge, for similar reasons. However, if I had jumped off a bridge and inexplicably survived, I would weigh that experience very heavily in future decisions with regard to whether or not to jump off bridges.

I don't ignore other people's reported experiences; I just consider my own experiences a far more reliable indicator of reality. This is partially because other people's experiences are by necessity incomplete; it's very hard for me to be sure that someone else has told me every detail that I would consider important about a given situation.

Since the burden of proof is on you; and since no evidence exists; are you not then compelled to disbelieve in the proposition ?

No. I am merely in no position to compel your belief in the proposition, and etiquette requires that I should not claim that the question is resolved in my favour. (Which it isn't). My options at this point are to either go out and gather evidence, or to drop the question entirely.

As I understand it, etiquette does permit you to assume that the question is resolved in favour of the null hypothesis; but without proof, you cannot compel my disbelief in the proposition.

What makes you think that the best explanation for all the fact is, in fact, "a miracle occurred", as opposed anything else ? Given that other events (honest mistakes, deliberate fraud, etc.) occur much more often than miracles (i.e., they have higher priors); and given that the evidence is compatible with all of these explanations; why do you keep the "miracle" explanation and discard the others ?

I don't discard all the others; I simply consider them less probable than the miracle hypothesis. And the reason for that is that a number of people whose job involves the investigation of miracles, and who have looked far more deeply into the matter than I have (and who would not benefit from incorrectly calling something a miracle and having it later revealedd as a mistake or a fraud) consider it a miracle. In short, I place my confidence in the hands of those I recognise as experts in the field.

That said experts were also largely members of the Catholic clergy does not diminish my confidence in their results, though it may affect yours.

There may have been millions more people who could have detected His actions, had they just looked in the right place, but they didn't... That was likely intentional...

Wait, doesn't this support what I said ? It sounds like your God does indeed make his actions "so subtle that no one has been able to detect them" (as I put it originally), just like my hypothetical Alpha-God.

No. Again, people have detected His actions. Consider Moses, for example; when Moses approached the burning bush, he detected God's actions.

Or consider the monk present at the Miracle of Lanciano; when he saw the bread and wine literally transform into flesh and blood, he detected God's actions.

Detectability is not necessary correlated with how much effect something has on our affairs.

How can something be completely undetectable and yet have any effect on anything ? Effects are how we detect things.

If it is completely undetectable by any means, then yes, it can have no effect. But something can be hard to detect while still having a great effect.

Consider, for example, a man living on a mountaintop. He finds it very easy to detect the stars; he sees them often. But they have little to no effect on him. On the other hand, he finds it very hard to detect the radioactivity of the rocks around him (he would need to go to the trouble of getting a geiger counter); but if the rocks are signifiantly radioactive, that could potentially have a very large long-term effect on him.

So, while I agree that something has to be detectable in order to have any effect (on the basis that it can be detected by its effect), it is nonetheless possible for something to be hard to detect while having a very large effect.