Edwards ea’s Bayesian Stats. Inf.

Edwards, W. L., Lindman, H. and Savage, L. J. (1963) Bayesian statistical inference for psychological research. Psychol. Rev., 70, 193-242

Probability is what you would bet on, without being vulnerable to Dutch Books.

PRINCIPLE OF STABLE ESTIMATION

  … The impact of actual vagueness and variability of prior probabilities differs greatly from one problem to another. They frequently have but negligible effect on the conclusions obtained from Bayes’ theorem … . If observations are precise, in a certain sense, relative to the prior distribution on which they bear, then the form and properties of the prior distribution have negligible influence on the posterior distribution. From a practical point of view, then, the untrammeled subjectivity of opinion about a parameter ceases to apply as soon as much data become available. More generally, two people with widely divergent prior opinions but reasonably open minds will be forced into arbitrarily close agreement about future observations by a sufficient amount of data. An advanced mathematical  expression of this phenomenon is in Blackwell and Dubins (1962).

Comment

Blackwell and Dubins is a purely mathematical result. To apply it one would need to be sure that one was dealing with phenomena that were accurately modelled by probability distributions in all respects. If your notion of probability is about current expectations, it is hard to see how you could make long-run conclusions. At best you could say that ‘rational’ minds (or ‘stats rats’) will be forced, now, to expect arbitrarily close agreement, not that they will actually get it.

Dave Marsay

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