◉ The Alleged Resurrection and Bayesian Variables: Priors, Likelihoods, Dependence, and the Cost of a Specific Miracle Claim

Public arguments for the bodily resurrection of Jesus often present early proclamation, appearance traditions, empty-tomb narratives, conversions, and movement growth as converging evidence. The Bayesian question is stricter: how much more expected is their joint record under a specific resurrection hypothesis than under a weighted mixture of non-resurrection pathways, given the relevant background information? This paper reconstructs that comparison at the variable level. The result is critical but bounded. The evidence can support early and sincere Easter belief, and some items may favor resurrection over particular rivals. Yet compatibility is not a Bayes factor, a broad theistic prior is not the prior of a first-century bodily resurrection, and correlated reports cannot be multiplied as independent confirmations. A defensible model must specify the deity's relevant intentions and disclosure policy, distinguish event evidence from downstream belief and narration, represent source dependence through joint conditional probabilities, and allocate weight across serious alternative combinations rather than defeat one convenient rival. Common public cases do not supply enough independent constraints to establish the posterior superiority they advertise. Different defensible settings for prior odds, reliability, dependence, and divine intent can reverse or greatly change the result. That underdetermination does not show that the resurrection did not occur, that no testimony matters, or that Bayesian reasoning mechanically settles history. It shows that the public inference must pay its full probabilistic costs before accumulation can count as confirmation.