Entropy and Uncertainty

Datos Bibliográficos

ID10706014
AutoresTeddy Seidenfeld (0000-0003-4828-2388, Carnegie Mellon University, autor de correspondencia)
Año1986
Volumen53
Número4
Páginas467-491
Fecha de publicación1986-12-01
Peer ReviewedSí
Open AccessSí
TipoARTICLE
RevistaPhilosophy of Science (JOURNAL)
Identificadores de la revistaISSN: 0031-8248 • E-ISSN: 1539-767X
EditorialCambridge University Press (CUP) (PUBLISHER)
DOI10.1086/289336
OpenAlexW4243742020
IdiomaEN
Citas recibidas14
Referencias citadas18

This essay is, primarily, a discussion of four results about the principle of maximizing entropy (MAXENT) and its connections with Bayesian theory. Result 1 provides a restricted equivalence between the two: where the Bayesian model for MAXENT inference uses an “a priori“ probability that is uniform, and where all MAXENT constraints are limited to 0–1 expectations for simple indicator-variables. The other three results report on an inability to extend the equivalence beyond these specialized constraints. Result 2 established a sensitivity of MAXENT inference to the choice of the algebra of possibilities even though all empirical constraints imposed on the MAXENT solution are satisfied in each measure space considered. The resulting MAXENT distribution is not invariant over the choice of measure space. Thus, old and familiar problems with the Laplacian principle of Insufficient Reason also plague MAXENT theory. Result 3 builds upon the findings of Friedman and Shimony (1971; 1973) and demonstrates the absence of an exchangeable, Bayesian model for predictive MAXENT distributions when the MAXENT constraints are interpreted according to Jaynes's (1978) prescription for his (1963) Brandeis Dice problem. Lastly, Result 4 generalizes the Friedman and Shimony objection to cross-entropy (Kullback-information) shifts subject to a constraint of a new odds-ratio for two disjoint events

Bayesian probability · Econometrics · Entropy (arrow of time) · Kullback–Leibler divergence · Principle of maximum entropy · Statistics · Computer Science · Decision-Making and Behavioral Economics · Mathematics · Philosophy and History of Science · Statistical Mechanics and Entropy