Theology, philosophy, math, science, and random other things

Bayesian evaluation for the likelihood of Christ's resurrection (Part 12)

My claim, at its heart, is very simple: the evidence of the many people claiming to have seen the risen Christ is abundantly sufficient to overcome any prior skepticism about a dead man coming back to life. My argument consists of backing up that statement with Bayesian reasoning and empirically derived probability values.

The emphasis on empirical probability values is important. Humans are notoriously bad at estimating probabilities, especially when the values reach extreme levels, like 1e-22. Some people, especially when discussing a controversial topic like the resurrection, will just pull numbers out of thin air to support their preconceptions. They'll make statements like "I'll grant a 23.599% chance that the disciples went to the wrong tomb". This can sometimes result in some pretty hilarious statements, like someone assigning a 1% chance for a generic conspiracy theory - as if they couldn't imagine anything less likely than a 1% probability.

This is why having an empirical bases for the probability values is crucial. Otherwise, you're likely to simply make up such worthless numbers, influenced only by your preconceived notions.

In my argument, none of the numbers I used are something I just made up. I gave each of them ample empirical backing. The two important numbers are the prior probability for the resurrection, and the Bayes' factor for a human testimony. I set the prior probability at 1e-22: this is, as I said, far more conservative than any requirement of empiricism. One may be able to empirically argue that nobody alive today has ever seen a man come back from the dead - this would set the prior odds at around 1e-9 or 1e-10. But I've gone much, much further. I've chosen the value of 1e-22 by taking the total number of all the humans that have ever lived, assumed that none of them have ever come back from the dead, then squaring the already tiny probability, just to handicap my argument further. There is no way to argue that it should be empirically set lower.

As for the Bayes' factor for a typical human testimony, I've set at 1e8. I've given numerous lines of thought that demonstrates that this is about the correct value. These including several examples from everyday life where you choose to trust someone, and the results of a natural experiment with the recent 1.6 billion dollar lottery. All these empirically derived lines of thinking converge around 1e8 as the correct value for the Bayes' factor of a typical human testimony.

But, this number is perhaps more difficult to accept than the prior probability. There is a large variance inherent in human testimony, and Bayes' factors are less familiar and less intuitive as a concept than a prior probability. For these reasons, I think it's worth demonstrating with a few more real-life examples that the Bayes' factors for a human testimony is really around 1e8.

We'll look at these examples in the coming weeks.

You may next want to read:
The want of a mate
How is God related to all other fields of study?
Another post, from the table of contents

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