The problem of translating prior information uniquely into a prior probability assignment represents the as yet unfinished half of probability theory, though the principle of maximum entropy in the preceding chapter provides one important tool. It is unfinished because it has been rejected for many decades by those who were unable to conceive of a probability distribution as representing information; but, just because of that long neglect, many current scientific, engineering, economic, and environmental problems are today calling out for new solutions to this problem, without which important new applications cannot proceed.

What are we trying to do?

It is curious that, even when different workers are in substantially complete agreement on what calculations should be done, they may have radically different views as to what we are actually doing and why we are doing it. For example, there is a large Bayesian community, whose members call themselves ‘subjective Bayesians’, who have settled into a position intermediate between ‘orthodox’ statistics and the theory expounded here. Their members have had, for the most part, standard orthodox training; but then they saw the absurdities in it and defected from the orthodox philosophy, while retaining the habits of orthodox terminology and notation.