Coherence graphs

Artificial Intelligence

Volumn 173, Issue 1, 2009, Pages 104-144

  Miranda, Enrique ^a   Zaffalon, Marco ^b  

^a UNIVERSIDAD REY JUAN CARLOS   (Spain)

^b DALLE MOLLE INSTITUTE FOR ARTIFICIAL INTELLIGENCE IDSIA   (Switzerland)

Author keywords

Coherent lower previsions; Graphical models; Probabilistic logic; Satisfiability; Walley's strong and weak coherence

Indexed keywords

BAYESIAN NETWORKS; BOOLEAN FUNCTIONS; COHERENT LIGHT; GRAPH THEORY; GRAPHIC METHODS; KETONES; PROBABILITY;

BAYESIAN; COHERENT LOWER PREVISIONS; COMPATIBILITY PROBLEMS; CREDAL NETWORKS; GRAPHICAL MODELS; GRAPHICAL REPRESENTATIONS; LOWER PREVISIONS; PROBABILISTIC ASSESSMENTS; SATISFIABILITY; TIME ALGORITHMS; WALLEY'S STRONG AND WEAK COHERENCE;

PROBABILITY DISTRIBUTIONS;

EID: 56549104902     PISSN: 00043702     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.artint.2008.09.001     Document Type: Article

References (38)

1. Antonucci A., and Zaffalon M. Decision-theoretic specification of credal networks: A unified language for uncertain modeling with sets of Bayesian networks. International Journal of Approximate Reasoning 49 2 (2008) 345-361
2. Arnold B., Castillo E., and Sarabia J.M. Conditional Specification of Statistical Models (1999), Springer
3. Baioletti M., Capotorti A., Tulipani S., and Vantaggi B. Elimination of Boolean variables for probabilistic coherence. Soft Computing 4 (2000) 81-88
4. Bhaskara Rao K.P.S., and Bhaskara Rao M. Theory of Charges (1983), Academic Press, London
5. Biazzo V., Gilio A., Lukasiewicz T., and Sanfilippo G. Probabilistic logic under coherence: Complexity and algorithms. Annals of Mathematics and Artificial Intelligence 45 1-2 (2005) 35-81
6. Boole G. An Investigation on the Laws of Thought, on Which are Founded the Mathematical Theories of Logic and Probabilities (1854), Walton and Maberley, London Reprinted by
7. Boole G. An Investigation on the Laws of Thought, on Which are Founded the Mathematical Theories of Logic and Probabilities (1961), Dover, New York
8. Capotorti A., and Vantaggi B. Locally strong coherence in inference processes. Annals of Mathematics and Artificial Intelligence 35 1-4 (2002) 125-149
9. Cozman F.G. Separation properties of sets of probabilities. In: Boutilier C., and Goldszmidt M. (Eds). Uncertainty in Artificial Intelligence (Proceedings of the Sixteenth Conference) (2000), Morgan Kaufmann, San Francisco 107-115
10. Cuadras C., Fortiana J., and Rodriguez-Lallena J.A. Distributions with Given Marginals and Statistical Modelling (2002), Kluwer Academic Publishers
11. de Finetti B. Sul significato soggettivo della probabilità. Fundamenta Mathematicae 17 (1931) 298-329
12. de Finetti B. La prévision: ses lois logiques, ses sources subjectives. Annales de l'Institut Henri Poincaré 7 (1937) 1-68 English translation in [18]
13. de Finetti B. Teoria delle Probabilità (1970), Einaudi, Turin
14. de Finetti B. Theory of Probability, vol. 1 (1974), John Wiley & Sons, Chichester English translation of [12]
15. Fréchet M. Sur les tableaux de correlation dont les marges sont donns. Ann. Univ. Lyon, Section A, Series 3 14 (1951) 53-77
16. Hansen P., Jaumard B., Poggi de Aragão M., Chauny F., and Perron S. Probabilistic satisfiability with imprecise probabilities. International Journal of Approximate Reasoning 24 2-3 (2000) 171-189
17. Hoeffding W. Masstabinvariante korrelationtheorie. Schriften des Mathematischen Instituts und des Institud für Angewndte Mathematik der Universität Berlin 5 (1940) 181-233
18. Jaumard B., Hansen H., and Poggi de Aragão M. Column generation methods for probabilistic logic. ORSA Journal on Computing 3 (1991) 135-148
19. In: Kyburg Jr. H.E., and Smokler H.E. (Eds). Studies in Subjective Probability (1964), Wiley, New York Second edition (with new material) 1980
20. Lukasiewicz T. Probabilistic deduction with conditional constraints over basic events. Journal of Artificial Intelligence Research 10 (1999) 199-241
21. Mauch F. On the existence of probability distributions with given marginals. Theory of Probability and its Applications 48 3 (2004) 541-548
22. E. Miranda, Updating coherent previsions on finite spaces, Technical Report TR 08/04, Rey Juan Carlos University, Technical Reports on Statistics and Decision Sciences, 2008
23. E. Miranda, G. de Cooman, Coherence and independence in non-linear spaces, Technical Report TR 05/10, Rey Juan Carlos University, Technical Reports on Statistics and Decision Sciences, 2005
24. Miranda E., and de Cooman G. Marginal extension in the theory of coherent lower previsions. International Journal of Approximate Reasoning 46 1 (2007) 188-225
25. Moral S., and Cano A. Strong conditional independence for credal sets. Annals of Mathematics and Artificial Intelligence 35 1-4 (2002) 295-321
26. Nelsen R. An Introduction to Copulas (1999), Springer, New York
27. Nilsson N.J. Probabilistic logic. Artificial Intelligence 28 (1986) 71-87
28. Pearl J. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference (1988), Morgan Kaufmann, San Mateo, CA
29. Sklar A. Fonctions de répartition à n-dimensions et leurs marges. Publications de l'Institute de Statistique de l'Université de Paris 8 (1959) 229-231
30. Tarjan R.E. Depth-first search and linear graph algorithms. SIAM Journal on Computing 1 (1972) 146-160
31. Troffaes M.C.M., and de Cooman G. Extension of coherent lower previsions to unbounded random variables. Intelligent Systems for Information Processing: For Information to Applications (2003), North Holland, Amsterdam 277-288
32. van der Gaag L.C. Computing probability intervals under independency constraints. In: Bonissone P.P., Henrion M., Kanal L.N., and Lemmer J.F. (Eds). UAI '90: Proceedings of the Sixth Annual Conference on Uncertainty in Artificial Intelligence (1991), Elsevier 457-466
33. Vorobev N.N. Consistent families of measures and their extensions. Theory of Probability and its Applications VII 2 (1962) 147-163
34. Walley P. Statistical Reasoning with Imprecise Probabilities (1991), Chapman and Hall, London
35. Walley P., Pelessoni R., and Vicig P. Direct algorithms for checking consistency and making inferences for conditional probability assessments. Journal of Statistical Planning and Inference 126 (2004) 119-151
36. P.M. Williams, Notes on conditional previsions, Technical report, School of Mathematical and Physical Science, University of Sussex, UK, 1975. Reprinted in [36]
37. Williams P.M. Notes on conditional previsions. International Journal of Approximate Reasoning 44 3 (2007) 366-383
38. M. Zaffalon, E. Miranda, Conservative inference rule for uncertain reasoning under incompleteness, 2008, submitted for publication