Daniel_Burfoot comments on Bayes' rule =/= Bayesian inference - Less Wrong

37 Post author: neq1 16 September 2010 06:34AM

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Comment author: Daniel_Burfoot 16 September 2010 02:07:14PM 4 points [-]

Good post. It might be worth mentioning, after noting the benefit of the Bayesian approach, the deep problem with it: the subjectivity of the prior. This can be illustrated by looking at one of the above paragraphs:

Based on experience and what I know about the laws of physics, I think it's very unlikely that your claim is accurate. I feel very confident that the probability is close to 0.5. However, I don't want to rule out something a little bit unusual (like a probability of 0.4).

It's fine for Bayesian A to choose a prior based on his experience, feelings, and intuitive reasoning. But it's equally reasonable for Bayesian B to assert a completely different prior for her own reasons. Then they will come to different conclusions based on identical evidence.

Comment author: jimrandomh 16 September 2010 03:28:25PM 8 points [-]

It's fine for Bayesian A to choose a prior based on his experience, feelings, and intuitive reasoning. But it's equally reasonable for Bayesian B to assert a completely different prior for her own reasons. Then they will come to different conclusions based on identical evidence.

Except that they're actually using different evidence, because the intuitive feelings that go into a prior are, in fact, evidence. More specifically, the prior is the sum of the outputs of all the heuristics that aren't quite strong or reliable enough to reach conscious awareness, but which nevertheless do, and ought to, influence the probability judgment.

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