1968/01/01 by E. T. Jaynes, Edwin Jaynes · 7 citations
Arts and Humanities · Computer Science · Mathematics · Physics and Astronomy · #Ambiguity #Applied mathematics #Arbitrariness #Basis (linear algebra) #Bayesian Modeling and Causal Inference #Calculus (dental) #Computer science #Consistency (knowledge bases) #Discrete mathematics #Entropy (arrow of time) #Invariant (physics) #Mathematical analysis #Mathematics #Monotonic function #Philosophy and History of Science #Principle of maximum entropy #Probability distribution #Quantum Mechanics and Applications #Statistics
paper · doi:10.1109/tssc.1968.300117
crossref issued 1968/01/01 · crossref published 1968/01/01 · crossref published-print 1968/01/01 · openalex publication_date 1968/01/01 · crossref created 2008/07/18 · crossref deposited 2022/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/24 · crossref indexed 2026/08/07
In decision theory, mathematical analysis shows that once the sampling distribution, loss function, and sample are specified, the only remaining basis for a choice among different admissible decisions lies in the prior probabilities. Therefore, the logical foundations of decision theory cannot be put in fully satisfactory form until the old problem of arbitrariness (sometimes called "subjectiveness") in assigning prior probabilities is resolved. The principle of maximum entropy represents one step in this direction. Its use is illustrated, and a correspondence property between maximum-entropy probabilities and frequencies is demonstrated. The consistency of this principle with the principles of conventional "direct probability" analysis is illustrated by showing that many known results may be derived by either method. However, an ambiguity remains in setting up a prior on a continuous parameter space because the results lack invariance under a change of parameters; thus a further principle is needed. It is shown that in many problems, including some of the most important in practice, this ambiguity can be removed by applying methods of group theoretical reasoning which have long been used in theoretical physics. By finding the group of transformations on the parameter space which convert the problem into an equivalent one, a basic desideratum of consistency can be stated in the form of functional equations which impose conditions on, and in some cases fully determine, an "invariant measure" on the parameter space.