At long last, we can summarize this entire series.
First, we calculated the prior odds for the resurrection of Jesus Christ. This prior cannot be zero. That would violate one of the fundamental tenets of Bayesian thinking, and it is not empirically justified, since we have not observed an infinite number of people who did not come back from the dead. Instead, empiricism demands that this prior be about the same as the reciprocal of the total number of non-resurrecting people we have observed, even if we have observed zero resurrections. Rather generously, this could be placed at 1e-11 - roughly corresponding to observing the non-resurrection of the total number of humans that have ever lived.
Second, we calculated the Bayes' factor for an earnest, insistent human testimony. Human testimony has value. This is not just an opinion or a hypothesis: human testimony must have value because your odds for an event actually changes when someone makes a testimony. Therefore, it must have a Bayes' factor. Thus the value of a human testimony can be calculated on a mathematical and empirical footing. As it turns out, for a testimony like the ones concerning Jesus's resurrection, the Bayes' factor is about 1e8. This is validated by multiple empirical observations, natural experiments, and thought experiments. There are several ways to modify this value depending on the exact nature of the testimony, which include things like dependency factors, an incentive to lie, and the "license plate effect". All of these can be understood and were taken into account.
We next evaluated the amount of evidence for Jesus's resurrection. Just from a stripped-down version of the testimonies summarized in 1 Corinthians 15, we saw that Peter, James, Paul, the 12 disciples, and a crowd numbering more than 500 all testified to Jesus's resurrection. Applying the Bayes' factor calculated above - with the appropriate modifications - to this set of evidence gave an enormous Bayes' factor, easily enough to completely overwhelm the prior odds of 1e-11 against the resurrection. We therefore concluded that Jesus almost certainly rose from the dead.
This calculation was then double checked against other historical reports of a resurrection. By comparing with the non-Christian resurrection reports, we saw that the level of evidence behind Jesus's resurrection is a clear outlier, to an absolutely absurd degree. This comparison therefore validated our earlier conclusion that Jesus rose from the dead.
Furthermore, because of the nature of this calculation, its conclusion is immune from many of the common skeptical arguments against the resurrection. The various possibilities - all the likely ways that the testimonies could have been wrong - have been already taken into account. No amount of speculation about how the resurrection reports could have been generated by naturalistic chance has any effect on the conclusion. We don't need to play 'what-if whack-a-mole' against the skeptic's speculations. This is a Bayesian argument. Speculations do absolutely nothing against it. Only evidence moves the odds.
However, because the Bayes' factor for Jesus's resurrection is so large, we then had to start worrying about crackpot theories - conspiracies, vivid mass hallucinations, alien interference, and the like. At the level of certainty which was implied by our calculation, we had to take even such things into account. This required a recalculation, specifically to take into account the near-total interdependency of evidence implied by such theories.
Fortunately, we had the historical data about other resurrection reports. This allowed us to explicitly construct the "skeptic's distribution", which is the probability distribution that generates the other historical resurrection reports through naturalistic means. This construction explicitly took into account the possibility of crackpot theories. This is the distribution that the skeptic must use, if they are to hold on to empiricism and naturalism - for this distribution incorporates the empirical, historical results of all such crackpot theories at the rate which actually occurred throughout history, and furthermore continues the distribution beyond the empirical end of the distribution using an exceedingly generous set of assumptions for the skeptic.
But even after taking even the crackpot theories into account, with a set of highly favorable assumptions for the skeptic, we saw that the Bayes' factor for the testimonies for Jesus's resurrection still enough to amply overpower the 1e-11 prior odds.
Furthermore, this was only after taking into account the raw amount of evidence summarized in 1 Corinthians 15. We did not take into account all the other people who testified to the resurrection in the New Testament (e.g. the women), and we did not take into account any of the strong pro-independence, anti-conspiracy properties of the testimonies (e.g. Paul's conversion). Including such factors would greatly strengthen an already nearly certain conclusion.
Therefore, this recalculation affirmed our previous conclusion: Jesus almost certainly rose from the dead.
As yet another double-check of our methodology, we tackled a number of other, non-Christian, non-resurrection miracle stories, using the same methodology. We reached the same conclusions that a skeptic would want us to reach - that probably nothing supernatural took place in these cases. Because this double-check reached the same conclusions as the skeptic, the skeptic must therefore count this as an additional validation of the methodology.
Furthermore, our methodology allows the Christian to say that the resurrection (and other Christian miracles) almost certainly took place, while at the same time consistently saying that the non-Christian miracles were probably not actually supernatural. The resurrection just has that much evidence behind it compared to non-Christian miracle stories.
But if anyone is still not convinced of Jesus's resurrection, I have the following challenge for them: naturalistically replicate the resurrection reports. Using the same means that were available to Jesus and his disciples - no political power, no great wealth, no modern science, etc. - generate multiple, detailed, independent, earnest, insistent personal testimonies from a great number of diverse types of people, unanimously testifying to a singular resurrection event. Furthermore, this must be achieved in spite of deadly persecution, in a fractious movement with no central control, along with a host of other difficulties and conditions. If you still doubt Jesus's resurrection, the scientific method demands that you take up this challenge.
Alternatively, you can follow the logic of the methodology outlined above, which is based on mathematics and empirical data, has been validated and double-checked multiple times, and gives the correct answer in all cases where the answer could be agreed upon. Short of embracing epistemological obliteration, you must accept its conclusion: Jesus almost certainly rose from the dead.
The next post is something a little different - a bit of an epilogue, and the future of this series.