Necessity of prior as common sense representation, especially when data cannot speak for themselves.
Prior information is essential also for a different reason, if we are trying to make inferences concerning which mechanism is at work. Fisher would, presumably, insist as strongly as any other scientist that a cause–effect relationship requires a physical mechanism to bring it about. But as in St Malo, the data alone are silent on this; they do not speak for themselves. Only prior information can tell us whether some hypothesis provides a possible mechanism for the observed facts, consistent with the known laws of physics. If it does not, then the fact that it accounts well for the data may give it a high likelihood, but cannot give it any credence. A fantasy that invokes the labors of hordes of little invisible elves and pixies running about to generate the data would have just as high a likelihood; but it would still have no credence for a scientist.
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Today, the question whether our present information does or does not provide credible evidence for the existence of a causal effect is a major policy issue, arousing bitter political, commercial, medical, and environmental contention, resounding in courtrooms and legislative halls. Yet cogent prior information – without which the issue cannot possibly be judged – plays little role in the testimony of ‘expert witnesses’ with orthodox statistical training, because their standard procedures have no place to use it.
– From Jaynes, E. T, Probability Theory: The Logic of Science
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