The null hypothesis is the elaborate conspiracy theory that you happen to share with all your peers.
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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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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As I said above: you often cannot collect enough observations to rule out a possibility.
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