This post displays up close the charts used in this Youtube video, which is a follow-up to this recent stream. In the video, which I won't try to reproduce here, I go into more detail about why it is important to use R and ~R in evaluating the evidence for the resurrection (that is, to compare the theory that the resurrection happened to the theory that it didn't happen) rather than comparing R only to some conjunction of specific, alternative explanations of the evidence (e.g., "Jesus didn't rise and the body was stolen and Peter had a hallucination and the stories in the Gospels were invented or embellished, etc.").
A partition, as I emphasize here and in the stream, is a set of mutually exclusive and jointly exhaustive propositions.
I argue that comparing the explanatory power of R to that of a "best naturalistic alternative" is epistemically uninformative and obscures the real evidential situation, as would be the case if one did something similar in any non-religious historical case. The video contains various perhaps-surprising probabilistic facts such as...Two incompatible theories can both be confirmed by a body of evidence. Just because there is an odds form of Bayes' Theorem without a partition, it doesn't follow that you can calculate the actual posterior probabilities of the two theories involved without using a partition.
Here are the images:
Odds form of Bayes' Theorem with a partition:
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