However, if a person were not already convinced that there is no such thing as immateriality, he/she would tend to take the Dr's word as to what happened and as to the likelihood of prior knowledge or lucky guesses.
No.
The whole point of science and scientific inquiry is that we do not take someone's word for it, especially when the implication is profound. It has nothing to do with some imagined bias that you're frantically trying to paste onto your critics. The rigor of scientific inquiry is meant to prune away even honest errors.
Your invitation to set aside reasonable and prudent skepticism and be inordinately credulous to your benefit is declined. Quit begging the question. Quit trying to suggest your critics are too biased to appreciate your genius.
You simply have no credible evidence. Understand that having no credible evidence means your claim fails, and that this is the way rational inquiry is supposed to work. Quit laboring under the delusion that you cannot possibly fail.
All I'm asking for agreement on is that the overall prior probability of immateriality be at least .001.
You don't need any rationale to declare your prior to be 0.001 in favor of immortality. You can do that simply because you think that's a nice round number, or because your cat meowed it too you. Ideally it should be based on some quantifiable reason, but as long as you obey certain other constraints, the prior can be arbitrary without loss of rigor.
But of course then you can't pull your something-over-infinity stunt on P(E|H). You wouldn't have a valid Bayesian model if you just guessed at both key factors. If you arbitrarily choose P(H) then P(E|H) needs to be quantitatively self-evident. Even a statistically inferential model has to have at least one foothold in reality in order to have any real-world value. So what it looks like you're trying to do is set up for an arbitrary P(E|H) by saying that P(H) is your foothold in fact. And you're trying to handwave up some putatively scientific rationale that would make your P(H) = 0.999 seem objectively justified instead of a number you just made up.
No.
You tell second- or third-hand ghost stories from a deceitful book that you beg people to accept at face value, even trying to shame them away from the healthy skepticism your book's track record should produce. You demonstrate absolutely no causal relationship between these stories and immortality, since they're
near-death experiences and not
after-death experiences. And then you beg your critics to give this wild ball of hearsay, speculation, and irresponsible attribution a statistical significance.
You are clearly unable to meet the rigor of a mathematical proof. You admit as much to Loss Leader. Now be a responsible human being and accept the consequences of these admissions.