E.T. Jaynes: Papers on Probability, Statistics, and Statistical PhysicsSpringer Science & Business Media, 30 avr. 1989 - 458 pages The first six chapters of this volume present the author's 'predictive' or information theoretic' approach to statistical mechanics, in which the basic probability distributions over microstates are obtained as distributions of maximum entropy (Le. , as distributions that are most non-committal with regard to missing information among all those satisfying the macroscopically given constraints). There is then no need to make additional assumptions of ergodicity or metric transitivity; the theory proceeds entirely by inference from macroscopic measurements and the underlying dynamical assumptions. Moreover, the method of maximizing the entropy is completely general and applies, in particular, to irreversible processes as well as to reversible ones. The next three chapters provide a broader framework - at once Bayesian and objective - for maximum entropy inference. The basic principles of inference, including the usual axioms of probability, are seen to rest on nothing more than requirements of consistency, above all, the requirement that in two problems where we have the same information we must assign the same probabilities. Thus, statistical mechanics is viewed as a branch of a general theory of inference, and the latter as an extension of the ordinary logic of consistency. Those who are familiar with the literature of statistics and statistical mechanics will recognize in both of these steps a genuine 'scientific revolution' - a complete reversal of earlier conceptions - and one of no small significance. |
Table des matières
1 INTRODUCTORY REMARKS | 1 |
2 INFORMATION THEORY AND STATISTICAL MECHANICS I 1957 | 4 |
3 INFORMATION THEORY AND STATISTICAL MECHANICS II 1957 | 17 |
4 BRANDEIS LECTURES 1963 | 39 |
5 GIBBS vs BOLTZMANN ENTROPIES 1965 | 77 |
6 DELAWARE LECTURE 1967 | 87 |
7 PRIOR PROBABILITIES 1968 | 114 |
8 THE WELLPOSED PROBLEM 1973 | 131 |
10 WHERE DO WE STAND ON MAXIMUM ENTROPY? 1978 | 210 |
11 CONCENTRATION OF DISTRIBUTIONS AT ENTROPY MAXIMA 1979 | 315 |
12 MARGINALIZATION AND PRIOR PROBABILITIES 1980 | 337 |
13 WHAT IS THE QUESTION? 1981 | 376 |
14 THE MINIMUM ENTROPY PRODUCTION PRINCIPLE 1980 | 401 |
SUPPLEMENTARY BIBLIOGRAPHY | 425 |
431 | |
9 CONFIDENCE INTERVALS vs BAYESIAN INTERVALS 1976 | 149 |
Autres éditions - Tout afficher
E. T. Jaynes: Papers on Probability, Statistics and Statistical Physics Edwin T. Jaynes Affichage d'extraits - 1983 |
E. T. Jaynes: Papers on Probability, Statistics and Statistical Physics R. D. Rosenkrantz Aucun aperçu disponible - 1983 |
Expressions et termes fréquents
analysis appear applications argument average B₂ Bayes Bayesian methods Bernoulli Boltzmann calculation complete ignorance condition confidence interval considered constraints correlations corresponding criterion defined definite density matrix determined E. T. Jaynes energy equal equilibrium ergodic estimate example experimental fact formalism frequency Gibbs give given hypothesis improper priors independent inference Information Theory integral equations intuitive invariance irreversible processes Jeffreys Jeffreys prior knowledge Laplace Laplace's lead macroscopic mathematical maximizes maximum entropy mean measure microstates nonequilibrium observed orthodox P₁ paradox partition function phase Phys physical possible posterior distribution posterior probability predictions principle of indifference principle of maximum prior information prior probabilities probability assignment probability distribution probability theory problem properties quantity question random experiment reason relevant represents result sampling distribution scale parameter second law sense solution specified statement statistical mechanics theorem thermodynamic tion transformation group uniform prior uninformative unique yields