So, for example, there's a story of Ichadon, an ancient Korean Buddhist monk. It's said that miraculous signs accompanying his death resulted in the adoption of Buddhism as the state religion. This story is recorded in the "Lives of Eminent Korean Monks" - about 700 years after the fact. As we've mentioned before, this kind of time gap makes any kind of personal testimony impossible, and the level of evidence here only reaches the "some people say..." level, which falls far short of overcoming the small prior against a genuine miracle.
In Islam, the Quran itself is said to be Muhammad's chief miracle - but it is difficult to evaluate this claim. We would need to dig into specific passages in the Quran and interpret it, which would easily end up leading down a rabbit hole. Otherwise, it's hard to say that the mere existence of the text is miraculous. Rather, we want a clear miracle - a miracle that can be recognized as such by anyone, like a resurrection. That is the point of a sign. After all, what good is a sign if it can't be clearly recognized?
The best known Islamic miracle of that kind - a miracle which is clearly a miracle - is Muhammad's splitting of the moon. But even this miracle is highly controversial. There are even certain interpretations - Islamic ones - which deny that this took place at all. They say that it is rather a prophecy that's suppose to take place at some future time.
The clearest case for the splitting of the moon being a literal miracle come from certain hadiths. Now, the sheer number of such citations and the authority they claim is indeed impressive - if one were to stop their investigation there.
But if you actually read these hadiths, you immediately notice how sparse they are in detail. For example, one of the more detailed hadiths on the subject reads:
We were along with God's Messenger at Mina, that moon was split up into two. One of its parts was behind the mountain and the other one was on this side of the mountain. God's Messenger said to us: Bear witness to this.And... that's it. Clearly, such a claim doesn't score particularly high on the "earnest and insistent" scale. Compare that to, say, the Gospel of John. The difference in the level of detail is incomparable.
It is furthermore worth noting that these hadiths were generally written down over two hundred years after Muhammad's death. They claim a chain of transmission going back to some contemporaries of Muhammad, but this chain often exceeds five or six people in length. They are therefore distinctly inferior to any of the testimonies in the New Testament in terms of their authenticity, just on this point alone.
Considering these facts, it's hard to see how these sparse testimonies add up to overcome the small prior odds against a miracle as remarkable as the moon splitting. A rough estimate would assign a Bayes' factor of ~ 1e1-1e3 for each of the 5 or so companions that were suppose to have originated some of the hadiths, giving an overall Bayes' factor of around 1e10, before taking dependence factors into account. Another way to think about this is to consider these hadiths to be parallel to the testimony of the group of apostles mentioned in 1 Corinthians 15, if we only had very sparse records of the apostles from over two hundred years after the fact. This again brings us to numbers far less than 1e10.
On the other hand, a miracle like splitting the moon is indeed highly remarkable - so it should at least be given a prior odds on par with the resurrection, of 1e-11. So the evidence just doesn't add up. A Bayes' factor of less than 1e10 doesn't overcome a prior odds of 1e-11. In addition, we must consider that there are no credible non-Islamic records of this highly visible and remarkable astronomical event, and the fact that there are good Islamic reasons to disbelieve that this ever happened. At the end of it all, we can be fairly confident that this did not actually happen as a miracle.
So, overall, we can say that our methodology does correctly reject non-Christian miracles. This validates the methodology for the skeptic's test cases, and therefore compels them to accept the results when the same methodology says that Jesus definitively rose from the dead.
Ah - but what about the other miracles in Christianity? Sure, the resurrection might be well-attested, but what about the numerous other miracles in the Bible which has barely any evidence behind it? For example, only Matthew mentions the resurrection of other people at the time of Jesus's death. He only mentions it in passing. Many of the miracles during the Exodus are mentioned only in that book. How could a Christian believe in such things, if such level evidence is inadequate according to our methodology?
This is where the "license plate effect" comes into play. Recall that human testimony can have absurdly high Bayes' factors, such as when you choose to believe a particular record of a chess game. There are over 1e120 possible chess games, so if you believe a particular game record, you're giving that game record a Bayes' factor of something like 1e120. How could a human testimony be so powerful?
It's because, even if the true game did not in fact go as recorded, there's no reason to believe that the mistake or the lie would result in that particular game record. Let's go through this step by step: P(game record|true game went according to the record) is high, because most games do in fact get recorded accurately. But P(game record|true game different from the record) is absurdly low - around 1e-120 - because even if the true game was actually different, there's no reason for the game record to end up as that particular incorrect record. But the ratio between these two probabilities is the Bayes' factor. In other words, the Bayes' factor explodes for human testimony, when there is no particular reason to pick that particular testimony. Or as Aron Wall put it, "this is a magical aspect of testimony, that it can cancel out any amount of low prior probability so long as it's merely due to there being large amount of detail".
Now, our Bayes' factor of genuine, sincere, insistent human testimony - 1e8 - was for cases where there already was a particular reason for a particular testimony. The collection of such testimonies in the New Testament was amply sufficient to cover the small prior odds against a resurrection, but it is not enough to cover the odds for all the miracles in the Bible.
But, that 1e8 is a minimum value. It can increase almost indefinitely, to values like 1e120 or more, once you accept the resurrection. Because once you accept that someone rose from the dead, it becomes a mere detail that the same person also healed the sick. It's just more details that his death triggered remarkable events. There's no reason for a lie or a mistake to record that particular miracle, if you're willing to accept that this is about the one who conquered the grave. In a similar vein, such a person is probably trustworthy when they vouch for the miraculous stories in Exodus. That is how all the other miracles in the Bible can be believed.
Let's go back to the chess game example. Let's say that a friend of yours claims to have beaten Magnus Carlsen, the current world chess champion. You initially say, "no way. You're nowhere good enough to beat the world champion". But many people, including large, independent, trustworthy groups, all publically, sincerely, and insistently state that your friend did in fact beat the world champion. Convinced by the overwhelming evidence, you eventually come to believe that this chess game actually took place, and that your friend actually won. For this decision, you should count the testimony of each individual as having a Bayes' factor of around 1e8, and the total evidence here must have been enough to overcome the small prior odds of your friend winning.
However, let's say your friend then gives you the record of this remarkable game. Should you believe this game record? Absolutely. You are now giving your friend an enormous Bayes' factor, of something like 1e120. The details - the exact record of the game - can be covered by human testimony, because there is no reason to doubt the record given that you've already accepted the unlikely results of the game. They are mere details, compared to your friend's remarkable victory. There is no reason for a lie or a mistake to result in this particular game record. This is what allows the Bayes' factor for the game record - 1e120 - to be far greater than the initial 1e8 that we gave to our friend's testimony. That is the "license plate effect", and it is what allows us to believe all the other miraculous stories in the Bible, once we accept Christ.
So, all that covers the numerous ways to test our methodology. It has passed them all. In everything there is perfect logical consistency and harmony. We believe all the things that ought to be believed, and reject all the things that ought to be rejected. And this methodology, which passes all the tests of the skeptics and the other religions, clearly concludes that Jesus Christ almost certainly rose from the dead.
You may next want to read:
Christians, read your Bibles
The Gospel: the central message of Christianity (part 1)
Another post, from the table of contents