Objective bayesianism and the maximum entropy principle

Entropy

Volumn 15, Issue 9, 2013, Pages 3528-3591

  Landes, Jürgen ^a   Williamson, Jon ^a  

^a UNIVERSITY OF KENT   (United Kingdom)

Author keywords

Bayesian conditionalisation; G entropy; Generalised entropy; Maxent; Minimax; Objective Bayesianism; Scoring rule; maximum entropy

Indexed keywords

EID: 84885365797     PISSN: None     EISSN: 10994300     Source Type: Journal    
DOI: 10.3390/e15093528     Document Type: Article

References (30)

1. Williamson, J. In Defence of Objective Bayesianism; Oxford University Press: Oxford, UK, 2010.
2. Jaynes, E.T. Information theory and statistical mechanics. Phys. Rev. 1957, 106, 620-630.
3. Grünwald, P.; Dawid, A.P. Game theory, maximum entropy, minimum discrepancy, and robust Bayesian decision theory. Ann. Stat. 2004, 32, 1367-1433.
4. Topsøe, F. Information theoretical optimization techniques. Kybernetika 1979, 15, 1-27.
5. Ramsey, F.P. Truth and Probability. In Studies in Subjective Probability; Kyburg, H.E., Smokler, H.E., Robert, E., Eds.; Krieger Publishing Company: Huntington, New York, NY, USA, 1926; pp. 23-52.
6. Shannon, C. A mathematical theory of communication. Bell Syst. Tech. J. 1948, 27, 379-423, 623-656. Reprinted with corrections. Available online: http://cm.bell-labs.com/cm/ms/what/ shannonday/shannon1948.pdf (accessed on 1 June 2013).
7. Aczél, J.; Daróczy, Z. On Measures of Information and Their Characterizations; Academic Press: New York, NY, USA, 1975.
8. Dawid, A.P. Probability Forecasting. In Encyclopedia of Statistical Sciences; Kotz, S., Johnson, N.L., Eds.; Wiley: New York, USA, 1986; Volume 7, pp. 210-218.
9. Joyce, J.M. Accuracy and Coherence: Prospects for an Alethic Epistemology of Partial Belief. In Degrees of Belief; Huber, F., Schmidt-Petri, C., Eds.; Synthese Library 342; Springer: Dordrecht, The Netherlands, 2009.
10. Pettigrew, R. Epistemic Utility Arguments for Probabilism. In The Stanford Encyclopedia of Philosophy; Zalta, E.N., Ed.; The Metaphysics Research Lab, Center for the Study of Language and Information, Stanford University: Stanford, CA, USA, 2011.
11. Predd, J.; Seiringer, R.; Lieb, E.; Osherson, D.; Poor, H.; Kulkarni, S. Probabilistic coherence and proper scoring rules. IEEE Trans. Inf. Theory 2009, 55, 4786-4792.
12. McCarthy, J. Measures of the value of information. Proc. Natl. Acad. Sci. USA 1956, 42, 654-655.
13. Shuford, E.H.; Albert, A.; Massengill, H.E. Admissible probability measurement procedures. Psychometrika 1966, 31, 125-145.
14. Aczel, J.; Pfanzagl, J. Remarks on the measurement of subjective probability and information. Metrika 1967, 11, 91-105.
15. Savage, L.J. Elicitation of personal probabilities and expectations. J. Am. Stat. Assoc. 1971, 66, 783-801.
16. Cover, T.M.; Thomas, J.A. Elements of Information Theory; Wiley: New York, NY, USA, 1991.
17. Ricceri, B. Recent Advances in Minimax Theory and Applications. In Pareto Optimality, Game Theory And Equilibria; Chinchuluun, A., Pardalos, P., Migdalas, A., Pitsoulis, L., Eds.; Optimization and Its Applications; Springer: New York, USA, 2008; Volume 17, pp. 23-52.
18. König, H. A general minimax theorem based on connectedness. Arch. Math. 1992, 59, 55-64.
19. Keynes, J.M. A Treatise on Probability; Macmillan: London, UK, 1948.
20. Williamson, J. From Bayesian epistemology to inductive logic. J. Appl. Logic 2013, in press, doi:10.1016/j.jal.2013.03.006.
21. Paris, J.B. The Uncertain Reasoner's Companion; Cambridge University Press: Cambridge, UK, 1994.
22. Seidenfeld, T. Entropy and uncertainty. Philos. Sci. 1986, 53, 467-491.
23. Williamson, J. An Objective Bayesian Account of Confirmation. In Explanation, Prediction, and Confirmation: New Trends and Old Ones Reconsidered; Dieks, D., Gonzalez, W.J., Hartmann, S., Uebel, T., Weber, M., Eds.; Springer: Dordrecht, The Netherlands, 2011; pp. 53-81.
24. Kyburg , H.E., Jr. Are there degrees of belief? J. Appl. Logic 2003, 1, 139-149.
25. Smets, P.; Kennes, R. The transferable belief model. Artif. Intell. 1994, 66, 191-234.
26. Keynes, J.M. The general theory of employment. Q. J. Econ. 1937, 51, 209-223.
27. Csisz'ar, I. Axiomatic characterizations of information measures. Entropy 2008, 10, 261-273.
28. Paris, J.B. Common sense and maximum entropy. Synthese 1998, 117, 75-93.
29. Paris, J.B.; Vencovská, A. A note on the inevitability of maximum entropy. Int. J. Approx. Reason. 1990, 4, 183-223.
30. Paris, J.B.; Vencovská, A. In defense of the maximum entropy inference process. Int. J. Approx. Reason. 1997, 17, 77-103.