Ok, I admit that science is hard. But about you ? How do you, personally, know what's a subversion of the natural order and what isn't ?

I have at least as much difficulty as the hypothetical scientist. Possibly slightly more difficulty, because the hypothetical scientist will know more science than I do.

Which possibility do you think is more likely in this case: genuine miracle, or mass confirmation bias ?

Insufficient data for a firm conclusion.

Opposing the mass confirmation bias hypothesis, are the claims that the water on the ground and on people's clothing was dried during the time; also apparently people 'miles away' (and thus unlikely to have been caught up in mass hysteria at the time) also reported having seen it.

Having said that, there is another explanation that occurs to me; the scene was described as the dancing sun appearing after a rainstorm, bursting through the clouds:

"As if like a bolt from the blue, the clouds were wrenched apart, and the sun at its zenith appeared in all its splendor."

If the clouds were thick enough, it may be hard to see the Sun; the bright light could have been... something else sufficiently hot and bright. (I do not know what, but there's room for a number of other hypotheses there).

I wouldn't venture a guess as to how much less than one, though.

Well, can you put a ballpark figure on it ? Do miracles happen (on average) once a year ? Once a century ? Once a millennium ? Once per the lifetime of our Universe ?

I am very poorly calibrated on such low frequencies, so take what I say here is highly speculative. (Also, the rate seems very variable, with several a year in the time of the Gospels, for example).

At a rough guess, I'd say possibly somewhere between once a year and once a century. Might be more, might be less.

I find a good deal of that external verification in the fact that a number of people, in whom I place a great deal of trust, and at least some of whom are known to be better at identifying truth than I am, have told me that it is true.

I think this is another difference between our methods; and I must confess that I find your approach quite weird. This doesn't automatically mean that it's wrong, of course; in fact, many theists (including C.S.Lewis) advocate it, so there might be something to it. I just don't see what.

Let me explain further, then, by means of an analogy. Consider the example you provide, of a trustworthy friend claiming to have found a great white shark in a nearby pond. For the sake of argument, I shall assume a rather large pond, in which a Great White could plausibly survive a day or two, but fed and drained by rivers too small for a Great White to swim along.

I shall further assume that you are aware that all your friends were on the fishing trip together (which you were unable to join due to a prior appointment).

Now, catching a Great White is a noteworthy accomplishment. If your friend were to accomplish this, it is reasonable to assign a high probability that he would tell you. Therefore, I assign the following:

P (Being told | Great White caught) = 0.95

It is also possible that your friends are collaborating on a prank, giving you an implausible story to see if they can convince you. If this is the case, they could have decided to do so while on the fishing trip, and laid out the necessary plans then. Exactly what probability you assign to this depends a lot on your friends; however, for the sake of argument, I shall assume that there's a 20% chance of this scenario.

P (Being told | No great white caught) = 0.2

Now, furthermore, there is no plausible way for a Great White to have ended up in the pond; and no plausible way to catch one with a simple fishing line. There are a variety of implausible but physically possible ways to accomplish both actions, though. So the prior probability of a Great White being caught is very low:

P (Great White caught) = 0.05

(possibly less than that, but let's go with that for the moment).

Thus, P(Being told) = P (Being told | Great White caught) P(Great White caught) + P (Being told | No great white caught) P(No great white caught) = (0.95 0.05) + (0.2 0.95) = 0.2375

Plugging this into Bayes, P(Great White caught | Being told) = P (Being told | Great White caught) P(Great White caught)/P(Being told) = (0.95 0.05)/0.2375 = 0.2

So, given certain assumptions about how trustworthy your friends are, etc., I find that the probability that they have indeed captured a Great White is higher if they tell you that they have than if they do not. Mind you, the prior probability for capturing a Great White is very low to begin with; the end result is still that it is more probable that they are lying than that they have captured a Great White, and you would be perfectly sensible to request further proof, in the form of the shark in question, before believing their claims.

So, is there a reason why you value empirical evidence as little as you do ? Alternatively, did I completely misunderstand your position ?

It's not that I completely discard empirical evidence; it's just that empirical evidence, one way or another, is somewhat rare in the case of this particular question, and thus I am forced to rely on what evidence I can find.

I have, on at least one occasion, observed some evidence; but it's the sort of evidence that doesn't communicate well and is rather unconvincing at one remove (I know it happened, because I remember it, but I have no proof other than my unsupported word).