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By Irving John Good
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Extra info for Good Thinking: The Foundations of Probability and Its Applications
But it remains a useful suggestion to help the mind in making judgments. ] New techniques arose out of the hierarchical suggestion, again apparently first in connection with the multinomial distribution (in the same paper), namely the concept of Type II maximum likelihood (maximization of the Bayes factor against the null hypothesis by allowing the hyperparameters to vary), and that of a Type II likelihood ratio for significance tests. I shall discuss these two concepts when discussing likelihood in general.
Building on this theme, the present work indicates how some apparently objective statistical techniques emerge logically from subjective soil, and can be further improved if their subjective logical origins (if not always historical origins) are not ignored. There should in my opinion be a constant interplay between the subjective and objective points of view, and not a polarization separating them. , "deciding in advance," the harmonic mean rule of thumb for significance tests in parallel, density estimation and roughness penalities, evolving probability and pseudorandom numbers and a connection with statistical mechanics.
B. Smith (1961), based on a justification by Ramsey (1926/31/50/64), de Finetti (1937/64), and L. J. Savage (1954) of a slightly different theory (in which sharp values of the probabilities and utilities are assumed). These justifications show that, on the assumption of certain compelling desiderata, a rational person will hold beliefs, and preferences, as //he had a system of subjective probabilities and utilities satisfying a familiar set of axioms. He might as well be explicit about it: after all it is doubtful whether any of our knowledge is better than of the "as if" variety.