Jeffreys 1939 and jaynes 1956 who worked in the field

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Unformatted text preview: all encompassing view of probability, not as an artefact, but as a basic way of reasoning about life, just as had Laplace. Jeffreys (1939) and Jaynes (1956) developed very clear ways of relating probabilities to what you know about the world around you, 21 ways that provide dramatic insights when applied to molecular processes that interest many physicists. However, Jaynes (1956) also showed that these ideas pay off handsomely when applied to inference problems in our macroscopic world (Howard, 1988). Frank Ramsey was the first to express an operational theory of action based on the dual intertwining notions of judgmental probability and utility. In his essay, Truth and Probability (1926) Ramsey adopted what is now termed the subjective or decision theoretic point of view. To Ramsey, probability is not the expression of a logical, rational, or necessary degree of belief, the view held by Keynes and Jeffreys, but rather an expression of a subjective degree of belief interpreted as operationally meaningful in terms of willingness to act (Raiffa, 1968). De Finetti in his essay, Foresight: Its Logical Laws, Its Subjective Sources originally published in 1937, like Ramsey, assessed a person’s degree of belief by examining his overt betting behaviour. By insisting that a series of bets be internally consistent or coherent such that a shrewd operator cannot make a sure profit or “book” regardless of which uncertain event occurs, De Finetti demonstrated that a person’s degrees of belief – his subjective probability assignments – must satisfy the usual laws of probability (Raiffa, 1968). Von Neumann and Morgenstern developed the modern probabilistic theory of utility in their second edition of Theory of Games and Economic Behaviour published in 1947. These authors, however, deal exclusively, with the canonical probabilities; that is, where each outcome is “equally likely”. Evidently, they were unaware of the work of Ramsey (Raiffa, 1968 p276). Abraham Wald formulated the basic problem of statistics as a problem of action. Wald (1964) analysed the general problem in terms of a normal form analysis (Raiffa, 1968 p277) and the problem he states reduces to selecting a best strategy for statistical experimentation and action when the true state of the world is unknown. Wald was primarily concerned with characterising those strategies for experimentation and action that are admissible or efficient for wide classes of prototypical statistical problems. Although Wald’s accomplishments were truly impressive, statistical practitioners were left in a quandary because Wald’s decision theory did not single out a best strategy but a family of admissible strategies, and in many important statistical problems this family is embarrassingly rich in possibilities. The practitioner wanted to know where to go from where Wald left off. How should he choose a course of action from the set of admissible contenders? The feeling of Wald and some of his associates was that while this is an important problem, it is...
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