{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:23:33Z","timestamp":1760243013933,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2015,3,27]],"date-time":"2015-03-27T00:00:00Z","timestamp":1427414400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Two open questions of inductive reasoning are solved: (1) does the principle of maximum entropy (PME) give a solution to the obverse Majern\u00edk problem; and (2) isWagner correct when he claims that Jeffrey\u2019s updating principle (JUP) contradicts PME? Majern\u00edk shows that PME provides unique and plausible marginal probabilities, given conditional probabilities. The obverse problem posed here is whether PME also provides such conditional probabilities, given certain marginal probabilities. The theorem developed to solve the obverse Majern\u00edk problem demonstrates that in the special case introduced by Wagner PME does not contradict JUP, but elegantly generalizes it and offers a more integrated approach to probability updating.<\/jats:p>","DOI":"10.3390\/e17041690","type":"journal-article","created":{"date-parts":[[2015,3,27]],"date-time":"2015-03-27T17:12:08Z","timestamp":1427476328000},"page":"1690-1700","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Maximum Entropy and Probability Kinematics Constrained by Conditionals"],"prefix":"10.3390","volume":"17","author":[{"given":"Stefan","family":"Lukits","sequence":"first","affiliation":[{"name":"Philosophy Department, University of British Columbia, 1866 Main Mall, Buchanan E370, Vancouver BC V6T 1Z1, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,3,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Jeffrey, R. (1965). The Logic of Decision, Gordon and Breach.","DOI":"10.2307\/2023748"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/S0034-4877(00)89030-8","article-title":"Marginal Probability Distribution Determined by the Maximum Entropy Method","volume":"45","year":"2000","journal-title":"Rep. Math. Phys."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Cover, T.M., and Thomas, J.A. (2006). Elements of Information Theory, Wiley.","DOI":"10.1002\/047174882X"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1667","DOI":"10.1109\/TIT.2005.846388","article-title":"MIMO Channel Modeling and the Principle of Maximum Entropy","volume":"51","author":"Debbah","year":"2005","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1093\/bjps\/37.4.453","article-title":"A Problem for Relative Information Minimizers, Continued","volume":"37","author":"Hughes","year":"1986","journal-title":"Br. J. Philos. Sci."},{"key":"ref_6","first-page":"280","article-title":"Optimal Information Processing and Bayes\u2019s Theorem: Comment","volume":"42","author":"Jaynes","year":"1988","journal-title":"Am. Stat."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"278","DOI":"10.1080\/00031305.1988.10475585","article-title":"Optimal Information Processing and Bayes\u2019s Theorem","volume":"42","author":"Zellner","year":"1988","journal-title":"Am. Stat."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1016\/j.inffus.2012.01.012","article-title":"Objective Priors from Maximum Entropy in Data Classification","volume":"14","author":"Palmieri","year":"2013","journal-title":"Inf. Fusion."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1002\/j.1538-7305.1948.tb00917.x","article-title":"A Mathematical Theory of Communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Tech. J."},{"key":"ref_10","unstructured":"Kullback, S. (1959). Information Theory and Statistics, Dover."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1214\/aoms\/1177729694","article-title":"On Information and Sufficiency","volume":"22","author":"Kullback","year":"1951","journal-title":"Ann. Math. Stat."},{"key":"ref_12","unstructured":"Guia\u00b8su, S. (1977). Information Theory with Application, McGraw-Hill."},{"key":"ref_13","unstructured":"Seidenfeld, T. (1986). Advances in the Statistical Sciences: Foundations of Statistical Inference, Springer."},{"key":"ref_14","first-page":"110","article-title":"Information et probabilit\u00e9","volume":"A 265","author":"Forte","year":"1967","journal-title":"Comptes rendus de l\u2019Acad\u00e9mie des sciences"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"131","DOI":"10.4064\/cm-9-1-131-150","article-title":"Information Without Probability","volume":"9","author":"Ingarden","year":"1962","journal-title":"Colloq. Math."},{"key":"ref_16","unstructured":"Khinchin, A. (1957). Mathematical Foundations of Information Theory, Dover."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"662","DOI":"10.1109\/TIT.1968.1054210","article-title":"Logical Basis for Information Theory and Probability Theory","volume":"14","author":"Kolmogorov","year":"1968","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1007\/BF00217475","article-title":"Generalized Probability Kinematics","volume":"36","author":"Wagner","year":"1992","journal-title":"Erkenntnis"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1007\/BF00873264","article-title":"Conditionalization and Observation","volume":"26","author":"Teller","year":"1973","journal-title":"Synthese"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1093\/bjps\/45.2.451","article-title":"Bayesian Conditionalization and Probability Kinematics","volume":"45","author":"Howson","year":"1994","journal-title":"Br. J. Philos. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1086\/341053","article-title":"Probability Kinematics and Commutativity","volume":"69","author":"Wagner","year":"2002","journal-title":"Phil. Sci."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Spohn, W. (2012). The Laws of Belief: Ranking Theory and Its Philosophical Applications, Oxford University.","DOI":"10.1093\/acprof:oso\/9780199697502.001.0001"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1214\/aoms\/1177698950","article-title":"Upper and Lower Probabilities Induced by a Multi-Valued Mapping","volume":"38","author":"Dempster","year":"1967","journal-title":"Ann. Math. Stat."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"620","DOI":"10.1103\/PhysRev.106.620","article-title":"Information Theory Statistical Mechanics","volume":"106","author":"Jaynes","year":"1957","journal-title":"Phys. Rev."},{"key":"ref_25","first-page":"299","article-title":"Information-Type Measures of Difference of Probability Distributions and Indirect Observations","volume":"2","year":"1967","journal-title":"Stud. Sci. Math. Hung."},{"key":"ref_26","unstructured":"Paris, J. (2006). The Uncertain Reasoner\u2019s Companion: A Mathematical Perspective, Cambridge University Press."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Caticha, A., and Giffin, A. (2006, January 8\u201313). Updating Probabilities. Paris, France.","DOI":"10.1063\/1.2423258"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1007\/BF01008275","article-title":"Jaynes\u2019s Maximum Entropy Prescription and Probability Theory","volume":"3","author":"Friedman","year":"1971","journal-title":"J. Stat. Phys."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1007\/BF00134086","article-title":"Updating, Supposing, and Maxent","volume":"22","author":"Skyrms","year":"1987","journal-title":"Theory Decis."},{"key":"ref_30","first-page":"223","article-title":"Can the Maximum Entropy Principle Be Explained as a Consistency Requirement?","volume":"26","author":"Uffink","year":"1995","journal-title":"Stud. Hist. Philos. Sci."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Walley, P. (1991). Statistical Reasoning with Imprecise Probabilities, Chapman and Hall.","DOI":"10.1007\/978-1-4899-3472-7"},{"key":"ref_32","unstructured":"Halpern, J. (2003). Reasoning About Uncertainty, MIT."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1111\/j.1520-8583.2010.00194.x","article-title":"A Defense of Imprecise Credences in Inference and Decision Making","volume":"24","author":"Joyce","year":"2010","journal-title":"Phil. Perspect."},{"key":"ref_34","unstructured":"Levine, R.D., and Tribus, M. (1978). The Maximum Entropy Formalism, MIT."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1093\/bjps\/31.2.131","article-title":"Bayesian Conditionalisation and the Principle of Minimum Information","volume":"31","author":"Williams","year":"1980","journal-title":"Br. J. Philos. Sci."},{"key":"ref_36","unstructured":"Zubarev, D., Vladimir, M., and Gerd, R. (1996). Statistical Mechanics of Nonequilibrium Processes, Akademie."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/4\/1690\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:44:01Z","timestamp":1760215441000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/4\/1690"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,3,27]]},"references-count":36,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2015,4]]}},"alternative-id":["e17041690"],"URL":"https:\/\/doi.org\/10.3390\/e17041690","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2015,3,27]]}}}