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Prior Probabilities
 IEEE Transactions on Systems Science and Cybernetics
, 1968
"... e case of location and scale parameters, rate constants, and in Bernoulli trials with unknown probability of success. In realistic problems, both the transformation group analysis and the principle of maximum entropy are needed to determine the prior. The distributions thus found are uniquely determ ..."
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e case of location and scale parameters, rate constants, and in Bernoulli trials with unknown probability of success. In realistic problems, both the transformation group analysis and the principle of maximum entropy are needed to determine the prior. The distributions thus found are uniquely determined by the prior information, independently of the choice of parameters. In a certain class of problems, therefore, the prior distributions may now be claimed to be fully as "objective" as the sampling distributions. I. Background of the problem Since the time of Laplace, applications of probability theory have been hampered by difficulties in the treatment of prior information. In realistic problems of decision or inference, we often have prior information which is highly relevant to the question being asked; to fail to take it into account is to commit the most obvious inconsistency of reasoning and may lead to absurd or dangerously misleading results. As an extreme examp
The Gibbs Paradox
, 1996
"... : We point out that an early work of J. Willard Gibbs (1875) contains a correct analysis of the "Gibbs Paradox" about entropy of mixing, free of any elements of mystery and directly connected to experimental facts. However, it appears that this has been lost for 100 years, due to some obsc ..."
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Cited by 18 (0 self)
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: We point out that an early work of J. Willard Gibbs (1875) contains a correct analysis of the "Gibbs Paradox" about entropy of mixing, free of any elements of mystery and directly connected to experimental facts. However, it appears that this has been lost for 100 years, due to some obscurities in Gibbs' style of writing and his failure to include this explanation in his later Statistical Mechanics. This "new" understanding is not only of historical and pedagogical interest; it gives both classical and quantum statistical mechanics a different status than that presented in our textbooks, with implications for current research. CONTENTS 1. INTRODUCTION 2 2. THE PROBLEM 3 3. THE EXPLANATION 4 4. DISCUSSION 6 5. THE GAS MIXING SCENARIO REVISITED 7 6. SECOND LAW TRICKERY 9 7. THE PAULI ANALYSIS 10 8. WOULD GIBBS HAVE ACCEPTED IT? 11 9. GIBBS' STATISTICAL MECHANICS 13 10. SUMMARY AND UNFINISHED BUSINESS 17 11. REFERENCES 18 y In Maximum Entropy and Bayesian Methods, C. R. Smith, G. J. E...
Quantum theory as inductive inference
, 2010
"... We present the elements of a new approach to the foundations of quantum theory and information theory which is based on the algebraic approach to integration, information geometry, and maximum relative entropy methods. It enables us to deal with conceptual and mathematical problems of quantum theory ..."
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Cited by 5 (5 self)
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We present the elements of a new approach to the foundations of quantum theory and information theory which is based on the algebraic approach to integration, information geometry, and maximum relative entropy methods. It enables us to deal with conceptual and mathematical problems of quantum theory without any appeal to Hilbert space framework and without frequentist or subjective interpretation of probability. PACS: 89.70.Cf 02.50.Cw 03.67.a 03.65.w 1
D. AN APPLICATION: IRREVERSIBLE STATISTICAL MIrHANIcS
, 1978
"... 71 74 78 80 86 88 90 93 95 ..."
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