Abstract
Our aim is to put under the right perspective the theory of stochastic independence in the framework of coherent probability theory, taking suitably into account also events whose probability is zero or one. Moreover, in a coherent setting, upper and lower probabilities come naturally to the fore, and so we discuss the issues raised when trying to extend stochastic independence to this more general concept.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
A. Capotorti and B. Vantaggi, Locally strong coherence in inference processes, Annals of Mathematics and Artificial Intelligence, this issue.
A. Capotorti, L. Galli and B. Vantaggi, How to use locally strong coherence in inferential processes based on lower-upper probabilities, Soft Computing (2001) in press.
G. Coletti, Coherent numerical and ordinal probabilistic assessments, IEEE Transactions on Systems, Man, and Cybernetics 24 (1994) 1747-1754.
G. Coletti, A. Gilio and R. Scozzafava, Conditional events with vague information in expert systems, in: Lecture Notes in Computer Sciences, Vol. 521, eds. B. Bouchon-Meunier, R.R. Yager and L.A. Zadeh (Springer, Berlin, 1991) pp. 106-114.
G. Coletti and R. Scozzafava, Characterization of coherent conditional probabilities as a tool for their assessment and extension, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 4 (1996) 103-127.
G. Coletti and R. Scozzafava, Conditional measures: old and new, in: Proceedings of New Trends in Fuzzy Systems, Napoli, 1996, eds. D. Mancini, M. Squillante and A. Ventre (World Scientific, Singapore, 1998) pp. 107-120.
G. Coletti and R. Scozzafava, Null events and stochastical independence, Kybernetika 34 (1998) 69-78.
G. Coletti and R. Scozzafava, Zero probabilities in stochastic independence, in: Information, Uncertainty, Fusion, eds. B. Bouchon-Meunier, R.R. Yager and L.A. Zadeh, Selected papers from IPMU 1998 (Kluwer, Dordrecht, 2000) pp. 185-196.
G. Coletti and R. Scozzafava, Conditioning and inference in intelligent systems, Soft Computing 3 (1999) 118-130.
G. Coletti and R. Scozzafava, The role of coherence in eliciting and handling "imprecise" probabilities and its application to medical diagnosis, Information Sciences 130 (2000) 41-65.
G. Coletti and R. Scozzafava, Stochastic independence for upper and lower probabilities in a coherent setting, in: Technologies for Constructing Intelligent Systems, Vol. 2, eds. B. Bouchon-Meunier, J. Gutiérrez-Rios, L. Magdalena, and R.R. Yager, Selected papers from IPMU 2000 (Springer, Berlin, 2001).
G. Coletti and R. Scozzafava, From conditional events to conditional measures: a new axiomatic approach, Annals of Mathematics and Artificial Intelligence 32, Special Issue on Representation of Uncertainty, ed. H. Greenberg (2001) 373-392.
G. Coletti, R. Scozzafava and B. Vantaggi, Probabilistic reasoning as a general unifying tool, in: Lecture Notes in Artificial Intelligence, Vol. 2143, eds. S. Benferhat and P. Besnard (Springer, Berlin, 2001) pp. 120-131.
I. Couso, S. Moral and P. Walley, Examples of independence for imprecise probabilities, in: International Symposium on Imprecise Probabilities and their Applications (ISIPTA '99) Ghent, Belgium (1999) pp. 121-130.
L.M. De Campos and S. Moral, Independence concepts for convex sets of probabilities, in: Uncertainty in Artificial Intelligence (UAI '95) (Morgan Kaufmann, San Mateo, CA, 1995) pp. 108-115.
B. de Finetti, Les probabilités nulles, Bulletin des Sciences Mathématiques 60 (1936) 275-288.
B. de Finetti, Sull'impostazione assiomatica del calcolo delle probabilità. Annali Univ. Trieste 19 (1949) 3-55. English translation in: Probability, Induction, Statistics (Wiley, London, 1972) chapter 5.
L.E. Dubins, Finitely additive conditional probabilities, conglomerability and disintegration, The Annals of Probability 3 (1975) 89-99.
P.H. Krauss, Representation of conditional probability measures on Boolean algebras, Acta Mathematica Hungarica 19 (1968) 229-241.
A. Rényi, On conditional probability spaces generated by a dimensionally ordered set of measures, Theory of Probability and its Applications 1 (1956) 61-71.
B. Vantaggi, Conditional independence in a finite coherent setting, Annals of Mathematics and Artificial Intelligence 32, Special Issue on Representation of Uncertainty, ed. H. Greenberg (2001) 287-313.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Coletti, G., Scozzafava, R. Stochastic Independence in a Coherent Setting. Annals of Mathematics and Artificial Intelligence 35, 151–176 (2002). https://doi.org/10.1023/A:1014535200933
Issue Date:
DOI: https://doi.org/10.1023/A:1014535200933