# subjective probability

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## subjective probability

[səb′jek·tiv ‚präb·ə′bil·əd·ē]
(statistics)
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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The coefficients for the subjective probability of an accident are positive and nearly statistically significant when the dependent variable is any accident in the last 3 years (p = 0.091, column (2), p = 0.069, column (3)).
If persons can express their expectations in probabilistic form, elicitation of subjective probability distributions should have compelling advantages relative to verbal questioning.
We observed significant differences between groups in rates of delay discounting [F(2, 87) = 5.090; p = 0.008; [[eta].sub.p.sup.2] = 0.10] but not in the rate of probability discounting [F(2, 87) = 0.983; p = 0.378; [[eta].sub.p.sup.2] = 0.02) or subjective probability of obtaining a delayed reward [F(2, 87)= 1.719; p = 0.185; [[eta].sub.p.sup.2] = 0.04).
People seem to believe that imposing liability based on circumstantial evidence is less appropriate even when the direct and circumstantial evidence do not differ in terms of the objective or subjective probability of the truth of the material facts, or in terms of their confidence in the probability assessment.
Responding to Wagner, Anatol Rapoport emphasizes the "formidable difficulty" in game theory of obtaining a "meaningful operational definition of subjective probability" and a "meaningful operational definition of utility," which "become insuperable in the context of nuclear deterrence." (10) Also responding to Wagner, Michael McGinnis criticizes the "implausibility of some of the underlying assumptions," especially the heavy computational burden required of decision makers to implement a game-theoretical analysis.
It is always possible to allocate a subjective probability. Sometimes allocating an experimental probability is not possible or very difficult or expensive.
The subject's perception of the outcome of the conflict choice situation is measured by a subjective probability. As is well known, subjective probabilities are applied to an event or outcome that is unique or occurs once.
Subjective probability judgments "represent the degree of rational belief that the speaker holds about the likelihood of occurrence of the event in question." (211) Subjective probability judgments are thus psychological, rather than strictly mathematical, judgments.
In fact, traditional bivalent probability (within which I include the doctrine of random chance as well as the much newer subjective probability) appears as a special case in this theory.
The need to measure subjective value has been around since the introduction of Expected Utility Theory by Bernoulli (1738/1954), and that of measuring subjective probability since the introduction of Subjective Expected Utility Theory by Savage (1954).
"[E]very physical probability," Good noted, "can be interpreted as a subjective probability or as a credibility." (1) This is a fascinating observation, because it raises the question why mathematicians and other scientists have spent so much time trying to establish that probability is a measure of something "objective" in the world if it has no bearing on the actual mathematics of probability.

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