Look, you’re going to have to decide what you are trying to argue. That God exists? That the resurrection took place? You can’t in the same argument both demonstrate the existence of God and that the resurrection took place and that God did it. Or well you can, it’s just that it’s going to become some colossal calculation and it has to start differently from indicated by Swamidass above.
If one is going to use the resurrection as evidence for God’s existence, one first needs to establish the probability that Jesus came back from the dead. That means the analysis has to start with the hypotheses:
H1: Jesus came back alive from being dead.
H2: Jesus did not come back alive from being dead.
To do that you need to start with the prior probability that someone would come back from the dead. That’s part of your background knowledge. How often do resurrections happen? The evidence for the resurrection (the purported testimonies) then feeds into that evaluation to raise the probability that the resurrection took place(presumably).
However, we also need to establish the probability that the testimony is reliable, we can’t just assume it’s genuine accounts and take them at face value. Here’s another problem: The better the evidence that Jesus died on the cross, the more unlikely it becomes that he was later seen alive. That’s how it works and will have to work, always, for anyone ever.
You disagree? Consider this analogy:
If you provide evidence that some person we know is in Australia this moment(maybe we get a broadcast from him where he’s walking around famous places in Sydney, and they show him live on Australian national television where he’s meeting the Australian prime minister), then any claim I make that he’s right next to me here in Denmark implies a conflict, because we have overwhelming evidence that people can’t be in two places at once.
Simply put, given the evidence we have that he’s in australia renders my claim instantly unbelievable, as in extremely unlikely to be true. And that is despite the fact that I am provably contemporaneous with the person, and I claim to be a direct witness delivering my own 1st-hand account. I should simply not be believed. If there were ten others like me, they should not be believed either. We would have to amass evidence other than our mere say-so.
Same way with the resurrection. Dead people stay dead(it is both the case God normally doesn’t seem to want to resurrect them, and they don’t naturally spring back alive), that’s our background knowledge. The better the evidence that Jesus died, the more unbeliavable the testimony of his postmortem appearances. As in they become less and less likely to be true. It should go without saying that unverifiable accounts(some of which are clearly copies and embellished) from millenia ago can’t overcome that, it’s absurd.
Another, further problem here is that the prior for coming back from the dead is between ≥0 and ≤1 in 100 billion. So we end up with a range for the prior, which means we will calculate a range for the posterior.
Once that has been done, the range of probability that Jesus came back from the dead, given the purported testimonial evidence (the reliability of which in turn also has to be established of course, and the better the evidence for his death, the more doubtful contradictory testimonials become, which means we would need extremely good testimonial evidence, meaning lots of verifiably independent 1st-hand accounts by people we have good reason to believe were eye-witnesses to the purported events), can then feed into another evaluation of the hypotheses:
H1A: God exists.
H2A: God does not exist.
We don’t have enough accounts, and we can’t verify their authenticity or independence.
If the probability that Jesus came back from the dead is greater than not it’s evidence for the existence of God, meaning it íncreases the posterior of God’s existence. How good that evidence is depends on how good the evidence for the resurrection is. But the evidence for the Jesus coming back alive is extremely weak, and it’s highly doubtful that it actually overcomes the evidence for Jesus being dead.