Classic analysis of the subject and the development of personal probability; one of the greatest controversies in modern statistcal thought.

"[This book] proposes new foundations for the Bayesian principle of rational action, and goes on to develop a new logic of desirability and probabtility."—Frederic Schick, _Journal of Philosophy_.

Degrees of belief; Dempster's rule of combination; Simple and separable support functions; The weights of evidence; Compatible frames of discernment; Support functions; The discernment of evidence; Quasi support functions; Consonance; Statistical evidence; The dual nature of probable reasoning.

First published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.

Richard Jeffrey's generalization of Bayes' rule of conditioning follows, within the theory of belief functions, from Dempster's rule of combination and the rule of minimal extension. Both Jeffrey's rule and the theory of belief functions can and should be construed constructively, rather than normatively or descriptively. The theory of belief functions gives a more thorough analysis of how beliefs might be constructed than Jeffrey's rule does. The inadequacy of Bayesian conditioning is much more general than Jeffrey's examples of uncertain perception (...) might suggest. The ``parameter α '' that Hartry Field has introduced into Jeffrey's rule corresponds to the "weight of evidence" of the theory of belief functions. (shrink)

A Probabilistic Information Processing System uses men and machines in a novel way to perform diagnostic information processing. Men estimate likelihood ratios for each datum and each pair of hypotheses under consideration or a sufficient subset of these pairs. A computer aggregates these estimates by means of Bayes' theorem of probability theory into a posterior distribution that reflects the impact of all available data on all hypotheses being considered. Such a system circumvents human conservatism in information processing, the inability of (...) men to aggregate information in such a way as to modify their opinions as much as the available data justify. It also fragments the job of evaluating diagnostic information into small separable tasks. The posterior distributions that are a PIP's output may be used as a guide to human decision making or may be combined with a payoff matrix to make decisions by means of the principle of maximizing expected value. A large simulation-type experiment compared a PIP with three other information processing systems in a simulated strategic war setting of the 1970's. The difference between PIP and its competitors was that in PIP the information was aggregated by computer, while in the other three systems, the operators aggregated the information in their heads. PIP processed the information dramatically more efficiently than did any competitor. Data that would lead PIP to give 99:1 odds in favor of a hypothesis led the next best system to give 4¿: 1 odds. (shrink)