Jacob Marschak and Others--Personal Probabilities of Probabilities
CALIFORNIA UNIV LOS ANGELES WESTERN MANAGEMENT SCIENCE INST
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By definition, the subjective probability distribution of a random event is revealed by the rational subjects choice between bets -- a view expressed by F. Ramsey, B. De Finetti, L.J. Savage and traceable to E. Borel and, it can be argued, to T. Bayes. Since hypotheses are not observable events, no bet can be made, and paid off, on a hypothesis. The subjective probability distribution of hypotheses or of a parameter, as in the current Bayesian statistical literature is therefore a figure of speech, an as if, justifiable in the limit. Given a long sequence of previous observations, the subjective posterior probabilities of events still to be observed are derived by using a mathematical expression that would approximate the subjective probability distribution of hypotheses, if these could be bet on. This position was taken by most, but not all, respondents to a Round Robin initiated by J. Marschak after M.H. DeGroots talk on Stopping Rules.
- Statistics and Probability