My point was that your prior must be informed by the previously existing evidence. For instance, if you don't have absolute evidence that vaccines cannot cause autism, your prior should be that some autism may be caused by vaccines and some may be not.
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Replying to @Plinz
Even with sampling the entire population, you probably cannot rule out that vaccines cause some autism. However, you may be able to quantify the probability of an upper bound (and compare that cost to the likely cost of not vaccinating).
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Replying to @Plinz
Even if different people choose different priors (A causes B, A may/may not cause B, A doesnt cause B), their priors would converge once the evidence is out. The only things that should be kept in mind is the priors could change.
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Replying to @dwindlinghandle
As I said above: you often cannot collect enough observations to rule out a possibility.
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Replying to @Plinz
Yes, the answer may not be yes/no. Your probability value would become your prior.
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Replying to @dwindlinghandle
If your null hypothesis is full independence, you might never collect enough evidence to leave it behind, if the factor is small enough, so your priors matter. If you model successively more interdependences, you may even miss the path into really fat optima.
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Replying to @Plinz
1. What do you mean by "null hypothesis is full independence"? Could you explain? 2. I think priors would matter in chaotic systems. But here ofcourse, choosing one's prior "wisely and cautiously", becomes the necessary thing.
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Replying to @dwindlinghandle
1. If you assume that vaccines cannot impair brain development (causally independent variables), and in 0.1% of children they do, your sample size may never be large enough to force you to change your null hypothesis, and you would miss the effect.
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Replying to @Plinz
2. “Carefully” means that there is a mathematically optimal way from counting all the bits on your interface to the universe. If you deviate from it, your world model is more likely to be wrong.
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Watch for signs that you have been born, it heralds imminent death within a few decades.
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