Partial knowledge, entropy, and estimation (prior

In a growing body of literature, available partial knowledge is used to estimate the prior probability distribution p (pi, . .. , p.) by maximizing entropy I(p) -Z2p1 log pi, subject to constraints on p which express that partial knowledge. The method has been applied to distribu- tions of income, of traffic, of stock- rice changes, and of types of brand-article purchases. We shall respond to two jus- tifications given for the method: (a) It is "conservative," and therefore good, to maximize "uncertainty," as (uniquely) represented by the entropy pa-rameter. (D) One should apply the mathematics of statistical thermo- dynamics, which implies that the most probable distribution has highest entropy. Reason (a) is rejected. Reason (8) is valid when "complete ignorance" is defined in a particular way and both the con- straint and the estimator's loss function are of certain kinds.