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Alex_Altair comments on An Intuitive Explanation of Solomonoff Induction - Less Wrong
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I would do the same thing I would do if my hay fever had gone away with no treatment.
And what would that be? Refuse to account for new evidence?
No, I mean I would be equally confused, because that's exactly what happened. Homeopathy is literally water, so I would be just as confused if I had drank water and my hay fever subsided.
Also, completely separately, even if you took some drug that wasn't just water, your case is anecdotal evidence. It should hold the same weight as any single case in any of the clinical trials. That means that it adds pretty much no data, and it's correct to not update much.
Ah, but that's not quite true. If a remedy helps you personally, it is less than a "single case" for clinical trial purposes, because it was not set up properly for that. You would do well to ignore it completely if you are calculating your priors for the remedy to work for you.
However, it is much more than nothing for you personally, once you have seen it working for you once. Now you have to update on the evidence. It's a different step in the Bayesian reasoning: calculating new probabilities given that a certain event (in this case one very unlikely apriori -- that the remedy works) actually happened.