To better frame my earlier point, suppose that you flare up six times during a season, and the six times it gets better after having applied “X” method which was statistically shown to be no better than placebo, and after rational analysis you find out that each time you applied method X you were also circumstantially applying method Y at the same time (that is, you’re also applying a placebo, since unless in your entire life you have never been relieved of some ailment by taking a pill, your body/brain will remember the principle and synchronize, just like any other form of positive reinforcement training).
In other words, both P(X-works|cured) and P(Y-works|cured) are raised, but only by half, since statistically they’ve been shown to have the same effect, and thus your priors are that they are equally as likely of being the cure-cause, and while both could be a cure-cause, the cure-cause could also be to have applied both of them. Since those two latter possibilities end up evening out, you divide the posteriors in the two, from my understanding. I might be totally off though, since I haven’t been learning about Bayes’ theorem all that long and I’m very much still a novice in bayesian rationality and probability.
To make a long story short, yes, I would stick to it, because within the presented context there are potentially thousands of X, Y and Z possible cure-causes, so while the likeliness that one of them is a cure is going up really fast each time I cure myself under the same circumstances, only careful framing of said circumstances will allow anyone to really rationally establish which factors become more likely to be truly causal and which are circumstantial (or correlated in another, non-directly-causal fashion).
Since homeopathy almost invariably involves hundreds of other factors, many of which are unknown and some of which we might be completely unaware, it becomes extremely difficult to reliably test for its effectiveness in some circumstances. This is why we assign greater trust in the large-scale double-blind studies, because our own analysis is of lower comparative confidence. At least within the context of this particular sniper example.
To better frame my earlier point, suppose that you flare up six times during a season, and the six times it gets better after having applied “X” method which was statistically shown to be no better than placebo, and after rational analysis you find out that each time you applied method X you were also circumstantially applying method Y at the same time (that is, you’re also applying a placebo, since unless in your entire life you have never been relieved of some ailment by taking a pill, your body/brain will remember the principle and synchronize, just like any other form of positive reinforcement training).
In other words, both P(X-works|cured) and P(Y-works|cured) are raised, but only by half, since statistically they’ve been shown to have the same effect, and thus your priors are that they are equally as likely of being the cure-cause, and while both could be a cure-cause, the cure-cause could also be to have applied both of them. Since those two latter possibilities end up evening out, you divide the posteriors in the two, from my understanding. I might be totally off though, since I haven’t been learning about Bayes’ theorem all that long and I’m very much still a novice in bayesian rationality and probability.
To make a long story short, yes, I would stick to it, because within the presented context there are potentially thousands of X, Y and Z possible cure-causes, so while the likeliness that one of them is a cure is going up really fast each time I cure myself under the same circumstances, only careful framing of said circumstances will allow anyone to really rationally establish which factors become more likely to be truly causal and which are circumstantial (or correlated in another, non-directly-causal fashion).
Since homeopathy almost invariably involves hundreds of other factors, many of which are unknown and some of which we might be completely unaware, it becomes extremely difficult to reliably test for its effectiveness in some circumstances. This is why we assign greater trust in the large-scale double-blind studies, because our own analysis is of lower comparative confidence. At least within the context of this particular sniper example.