Let us summarize the "skeptic's distribution" argument for Christ's resurrection.
We have already seen that any kind of reasonable investigation into Jesus's resurrection accounts would conclusively demonstrate that Jesus did rise from the dead. The only possibility left for the skeptic is to turn to unreasonable hypotheses - that is, to crackpot theories like conspiracies.
The distinguishing feature of these theories is that they postulate a near-total interdependence among the evidence, as if they were all manufactured by a single source - the conspiracy. This allows them to ignore the abundance of evidence for a certain position, and instead attribute it all to a rather unlikely prior.
Now, there are many excellent reasons to reject any kind of conspiracy theory when it comes to Jesus's resurrection. Just the conversion of Apostle Paul would be enough to put it beyond any realistic possibility. But that only scratches the surface of the many anti-conspiracy evidence available to the resurrection. However, we will not quantitatively consider these. We will merely use them to sandbag our conclusion - with the note that they would apply their full, independent force against the skeptic's position, since crackpot theories are all that the skeptic has left at this point.
So then, how do we quantitatively consider the interdependence of evidence, fully taking into account all the different possible crackpot theories?
We construct the "skeptic's distribution" - the probability distribution for achieving a certain level evidence for a resurrection, assuming a skeptical, anti-supernatural worldview. This probability distribution is actually quite accessible, since every single non-Christian resurrection report in world history would be the result of a sample drawn from it. Furthermore, such a distribution would fully take into account the aggregate of all the different types of crackpot theories that actually could have happened in history. The results of all things like conspiracy theories or religious mass delusions would show up in the samples, and the samples can then be extrapolated for things beyond what actually happened in history.
Once we have the "skeptic's distribution", the rest of the calculation is easy. We calculate the "skeptic's probability", which is the probability for the "skeptic's distribution" to generate at least a Jesus-level resurrection report. Since the corresponding "Christian's probability" is of order unity, the Bayes' factor for Jesus's resurrection is essentially the reciprocal of the "skeptic's probability".
We first constructed the "skeptic's distribution" using the most pro-skeptical assumptions possible. Even then, this gave "even odds" of Jesus's resurrection having taken place, under an impossibly favorable set of assumptions for skepticism.
Re-running the calculation with demonstrably more realistic - but still very conservative - assumptions, we saw that the Bayes' factor for Jesus's resurrection was still at least around 1e14 or 1e16. Against a prior of 1e-11 for someone rising from the dead, this puts the final odds for Jesus's resurrection at 1e3 to 1e5 - that is, somewhere between 99.9% to 99.999%. All this is with only part of the evidence for Christianity (those summarized in 1 Corinthians 15), and without considering any evidence that applies specifically against conspiracy theories.
The conclusion is clear: Jesus almost certainly rose from the dead.
We will begin a new line of thinking for the resurrection in the next post.
You may next want to read:
Adam and Eve were historical persons. Who were they? (Part 1)
Christianity and falsifiability
Another post, from the table of contents