Jacob Marschak and Others--Personal Probabilities of Probabilities
Abstract
By definition, the subjective probability distribution of a random event is revealed by the ('rational') subject's 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. DeGroot's talk on Stopping Rules.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1974
- Accession Number
- AD0781295
Entities
People
- Jacob Marschak
Organizations
- University of California, Los Angeles