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GabrielDuquette comments on A Rationalist's Tale - Less Wrong
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Can you elaborate? Were they explainable in retrospect?
I've got a similar story. A high school friend's grandmother took a trip to Sri Lanki (their home country) to visit a "healer" (they were Buddhist, but I don't know which kind) in a last-ditch effort to avoid death from cancer. She came back without her tumor. Can I explain this? No, I can't.
Well, we know that spontaneous remissions on cancers do occur, very rarely, but they do occur. One of the hypothesis is that the immune system finally learns to attack the cancer. With the huge number of people who, faced with a disease that scientific medicine doesn't know how to cure, go to prayer or healers, it's not surprising that, statistically, a few spontaneous remissions do happen just after such a visit. Especially considering the placebo effect, and the non-negligeable links between the efficiency of the immune system and the mental state (it's well known that stress diminish the efficiency of the immune system).
What would be meaningful is not a single case of unexplained spontaneous healing. It's a significant, reproducible, higher-than-placebo, increase in survival rate by a given healer (or a set of healers using a given faith). And that is, as far as I know, not backed by any study (or if it is, please show me the link).
That said, if you get the placebo effect from going to a faith healer, do it.
Unless you can get it cheaper ways...
Right. Moreover, of all the people who read GabrielDuquette's comment and know someone that had cancer and went to a faith healer, I imagine only the ones with a story like Jayson_Virisimo's will post a reply. Failed attempts are not reported. If you are acquaintances with someone that experienced a failed faith healing, you are likely not even aware of it! (If it was successful, they would have lauded it.) An easy Bayesian estimate makes the presence of Jayson_Virisimo's comment unsurprising.
Given a sufficiently non-zero probability of spontaneous remission, this argument explains my lack of surprise at such a story. This is an important addition to your argument (and, I feel, indeed the crux), because a non-zero probability is not satisfactory. Consider if we had many people posting such claims; with sufficiently low probabilities of spontaneous remission, we would not expect such a density of claims.
That sounds about right.
I would explain it as a spontaneous remission followed by the post hoc fallacy.
Edit: assuming, of course, that the tumor was actually gone, as DSimon points out.
Surely you mean, causing post hoc fallacy?
If I do that, I may be in danger of committing the post hoc fallacy :-)
That was the joke...
Indeed.
How did you know that the tumor was eliminated? That is, was there a before-and-after x-ray clearly showing the difference?
I don't know it was eliminated. My only evidence is my friend's testimony, his track record of truth-telling, and the fact the his was an atheist (and, therefore, unlikely to make up mystical stories to promote his religion).
Then what I really want to know is: how did your friend know the tumor was eliminated?
I'd like to second the question. Computational decision theoretic cosmology doesn't rule out statistical miracles and more importantly it's best to compute likelihood ratios and posteriors separately. E.g. see: http://www.overcomingbias.com/2009/02/share-likelihood-ratios-not-posterior-beliefs.html